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322 MILES Table 2 Sample Iteration Log MILES (July 1993) Ver:225-386-02 Thomas F. Rutherford Department of Economics University of Colorado Technical support available only by Email: TOM@GAMS.COM Work space allocated -- 0.01 Mb Initial deviation ........ 3.250E+02 P_01 Convergence tolerance .... 1.000E-06 0 3.25E+02 1.00E+00 (P_01 ) 1 1.14E-13 1.00E+00 (W_02 ) Major iterations ........ 1 Lemke pivots ............ 10 Refactorizations ........ 2 Deviation ............... 1.137E-13 Solved. Work space allocated -- 0.01 Mb Initial deviation ........ 5.750E+02 W_02 Convergence tolerance .... 1.000E-06 0 5.75E+02 1.00E+00 (W_02 ) 1 2.51E+01 1.00E+00 (P_01 ) 2 4.53E+00 1.00E+00 (P_01 ) 3 1.16E+00 1.00E+00 (P_01 ) 4 3.05E-01 1.00E+00 (P_01 ) 5 8.08E-02 1.00E+00 (P_01 ) 6 2.14E-02 1.00E+00 (P_01 ) 7 5.68E-03 1.00E+00 (P_01 ) 8 1.51E-03 1.00E+00 (P_01 ) 9 4.00E-04 1.00E+00 (P_01 ) 10 1.06E-04 1.00E+00 (P_01 ) 11 2.82E-05 1.00E+00 (P_01 ) 12 7.47E-06 1.00E+00 (P_01 ) 13 1.98E-06 1.00E+00 (P_01 ) 14 5.26E-07 1.00E+00 (P_01 ) Major iterations ........ 14 Lemke pivots ............ 23 Refactorizations ........ 15 Deviation ............... 5.262E-07 Solved.
MILES 323 6 Status File Output The status file reports more details regarding the solution process than are provided in the log file. Typically, this file is written to disk and examined only if a problem arises. Within GAMS, the status file appears in the listing only following the GAMS statement ”OPTION SYSOUT=ON;”. The level of output to the status file is determined by the options passed to the solver. In the default configuration, the status file receives all information written to the log file together a detailed listing of all switches and tolerances and a report of basis factorization statistics. When output levels are increased from their default values using the options file, the status file can receive considerably more output to assist in debugging. Tables 3-6 present a status file generated with LEVOUT=3 (maximum), PIVLOG=T, and LCPECH=T. The status file begins with the same header as the log file. Thereafter is a complete echo-print of the user-supplied option file when one is provided. Following the core allocation report is a full echo-print of control parameters, switches and tolerance as specified for the current run. Table 4 continues the status file. The iteration-by- iteration report of variable and function values is produced whenever LEVOUT >= 2. Table 4 also contains an LCP echo-print. This report has two sections: $ROWS and $COLUMNS. The four columns of numbers in the $ROWS section are the constant vector (q), the current estimate of level values for the associated variables (z), and the lower and upper bounds vectors (l and u). The letters L and U which appear between the ROW and Z columns are used to identify variables which are non-basic at their lower and upper bounds, respectively. In this example, all upper bounds equal +∞ , so no variables are non-basic at their upper bound. By convention, only variable (and not equation names) appear in the status file. An equation is identified by the corresponding variable. We therefore see in the $COLUMNS: section of the matrix echo-print, the row names correspond to the names of z variables. The names assigned to variables z i , w i and v i are z− , w− , and v− , as shown in the $COLUMNS section. The nonzeros for w− and v− variables are not shown because they are assumed to be −/ + I. The status file output continues on Table 5 where the first half of the table reports output from the matrix scaling procedure, and the second half reports the messages associated with initiation of Lemke’s procedure. The ”lu6chk warning” is a LUSOL report. Thereafter are two factorization reports. Two factorizations are undertaken here because the first basis was singular, so the program install all the lower bound slacks in place of the matrix defined by the initial values, z. Following the second factorization report, at the bottom of Table 5 is a summary of initial pivot. ”Infeasible in 3 rows.” indicates that ˜h contains 3 nonzero elements. ”Maximum infeasibility” reports the largest amount by which a structural variable violates an upper or lower bound. ”Artificial column with 3 elements.” indicates that the vector h = B 0˜h contains 3 elements (note that in this case B 0 = −I because the initial basis was singular, hence the equivalence between the number of nonzeros in ˜h and h.). Table 6 displays the final section of the status file. At the top of page 6 is the Lemke iteration log. The columns are interpreted as follows: ITER is the iteration index beginning with 0, STATUS is a statistic representing the efficiency of the Lemke path. Formally, status is the ratio of the minimum number of pivots from B 0 to the current basis divided by the actual number of pivots. When the status is 1, Lemke’s algorithm is performing virtually as efficiently as a direct factorization (apart from the overhead of basis factor updates.) Z% indicates the percentage of columns in the basis are ”structural” (z’s). Z0 indicates the value of the artificial variable. Notice that in this example, the artificial variable declines monotonically from its initial value of unity. ERROR is a column in which the factorization error is reported, when it is computed. For this run, ITCH=30 and hence no factorization errors are computed.
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GAMS — The Solver Manuals c○ 20
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4 CONTENTS
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6 Basic Solver Usage Option iterlim
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8 Basic Solver Usage keyword(s) [mo
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10 AlphaECP 1.2 Running GAMS/AlphaE
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12 AlphaECP A: Infeasible, deleted
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14 AlphaECP 0 Never. 1 Call the NLP
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16 AlphaECP mipoptcr (real) Relativ
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18 AlphaECP Westerlund T. and Pette
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20 BARON 1.1 Licensing and software
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22 BARON on probing : 000:00:00, in
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24 BARON 4.2 Finding the best, seco
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26 BARON in the form of solver boun
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28 BARON 5.4 Range reduction option
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30 BARON 5.6 Heuristic local search
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32 BARON Option Description Default
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34 BDMLP
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36 BENCH option modeltype=bench; Th
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38 BENCH Option Description Default
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40 BENCH In the example below, EXAM
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42 BENCH --- Spawning solver : CPLE
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44 BENCH To terminate not only the
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46 BENCH
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48 COIN-OR also found their way int
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50 COIN-OR This sets the algorithm
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52 COIN-OR Option type default B-BB
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54 COIN-OR integer tolerance: Set i
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56 COIN-OR stop diving on cutoff: F
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58 COIN-OR userjobid: Postfixes gdx
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60 COIN-OR nlp solve max depth: Set
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62 COIN-OR maxmin crit no sol: Weig
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64 COIN-OR General Options iterlim
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66 COIN-OR This option causes GAMS
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68 COIN-OR scaling (string) Scaling
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70 COIN-OR sos This option let CBC
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72 COIN-OR knapsackcuts (string) De
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74 COIN-OR 1 Turns the feasibility
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76 COIN-OR userheurmult (integer) D
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78 COIN-OR This option determines t
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80 COIN-OR noiterlim (integer) Allo
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82 COIN-OR linear_solver pardiso pa
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84 COIN-OR # This is a comment # Tu
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86 COIN-OR acceptable tol: ”Accep
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88 COIN-OR slack bound push: Desire
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90 COIN-OR linear system scaling: M
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92 COIN-OR mumps pivtol: Pivot tole
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94 COIN-OR fixed variable treatment
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96 COIN-OR adaptive mu monotone ini
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98 COIN-OR quality function balanci
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100 COIN-OR alpha min frac: Safety
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102 COIN-OR • no: don’t skip
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104 COIN-OR max resto iter: Maximum
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106 COIN-OR • no: perturbation on
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108 COIN-OR 6.2 Usage of CoinScip T
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110 COIN-OR gams/usergdxname (strin
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112 CONOPT 1 Introduction Nonlinear
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114 CONOPT 130 0 103 2.1776589484E+
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116 CONOPT The two messages above t
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118 CONOPT CONOPT time Total 0.109
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120 CONOPT 6 Hints on Good Model Fo
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122 CONOPT by the reduced complexit
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124 CONOPT of 4.1**2, which means t
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126 CONOPT X.SCALE(I,J,K)$IJK(I,J,K
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128 CONOPT delta. The error is redu
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130 CONOPT the NLP solver will comp
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132 CONOPT The relationship between
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134 CONOPT A : ❅ ❅ ❅ ❅ Zero
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136 CONOPT EQUATION E1, E2, E3, E4;
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138 CONOPT unfortunate that a redun
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140 CONOPT The Crash procedure is n
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142 CONOPT infeasible equations (th
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144 CONOPT The steepest edge proced
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146 CONOPT CONOPT will after the pr
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148 CONOPT X2 appearing in E2: Pivo
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150 CONOPT Until a final solution h
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152 CONOPT Option Description Defau
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154 CONOPT Option Description Defau
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156 CONOPT
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158 CONVERT • LindoMPI • LINGO
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160 CONVERT Option Description Defa
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162 CPLEX 11 2 How to Run a Model w
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164 CPLEX 11 • You can collect al
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166 CPLEX 11 individual GDX solutio
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168 CPLEX 11 parallelmode predual p
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170 CPLEX 11 mipordind mipordtype m
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172 CPLEX 11 6 Special Notes 6.1 Ph
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174 CPLEX 11 Start. The number of t
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176 CPLEX 11 Aggregator did 30 subs
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178 CPLEX 11 Nodes Cuts/ Node Left
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180 CPLEX 11 baritlim (integer) Det
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182 CPLEX 11 -1 Do not generate cov
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184 CPLEX 11 .divflt (real) A diver
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186 CPLEX 11 feasoptmode (integer)
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188 CPLEX 11 implbd (integer) Deter
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190 CPLEX 11 wasted computation tim
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192 CPLEX 11 netppriind (integer) N
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194 CPLEX 11 Settings of this paral
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196 CPLEX 11 1 Force node presolve
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198 CPLEX 11 repairtries (integer)
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200 CPLEX 11 simdisplay (integer) T
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202 CPLEX 11 populate procedure aga
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204 CPLEX 11 1 Display standard min
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206 CPLEX 11
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208 DECIS 1 DECIS 1.1 Introduction
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210 DECIS 1.4 Solving the Universe
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212 DECIS SMPS (stochastic mathemat
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214 DECIS statement would work as w
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216 DECIS RHS demand m 1000.00 peri
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218 DECIS omega1 defines all realiz
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220 DECIS nzrows — Number of rows
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222 DECIS Example The following exa
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224 DECIS 20 0.2464E+05 0.2464E+05
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226 DECIS pro 0.1 0.2 0.5 0.1 0.1 ;
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228 DECIS parameter hm2(dl) / h 100
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230 DECIS 15. ERROR: error code: in
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232 DECIS REFERENCES DECIS License
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234 DICOPT Although the algorithm h
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236 DICOPT where λ i is the Lagran
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238 DICOPT option rminlp=minos; sol
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240 DICOPT **** ERRORS(S) IN EQUATI
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242 DICOPT * stop only on infeasibl
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244 DICOPT mipoptfile s 1 s 2 . . .
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246 DICOPT nlptracelevel 3 As nlptr
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248 DICOPT --- DICOPT: Checking con
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250 DICOPT NLP 2 1.72097< 0.00 3 0
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252 DICOPT • The GAMS option stat
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254 DICOPT REFERENCES
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256 EMP
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258 EXAMINER The optimality checks
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260 EXAMINER Option Description Def
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262 EXAMINER
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264 GAMS/AMPL --- No AmplPath optio
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266 GAMS/LINGO --- No LingoPath opt
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268 KNITRO • Derivative-free, 1st
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270 KNITRO Option Description Defau
Page 272 and 273: 272 KNITRO Option Description Defau
Page 274 and 275: 274 KNITRO If outlev=2, information
Page 276 and 277: 276 KNITRO (Dense) Quasi-Newton BFG
Page 278 and 279: KNITRO References [1] R. H. Byrd, J
Page 280 and 281: 280 LGO GAMS/LGO does not rely on a
Page 282 and 283: 282 LGO 3 The GAMS/LGO Log File The
Page 284 and 285: 284 LGO Illustrative References R.
Page 286 and 287: 286 LINDOGlobal report the best one
Page 288 and 289: 288 LINDOGlobal Infeasibility of be
Page 290 and 291: 290 LINDOGlobal MIP AOPTTIMLIM time
Page 292 and 293: 292 LINDOGlobal 4.5 NLP Options NLP
Page 294 and 295: 294 LINDOGlobal 3 Decomposed model
Page 296 and 297: 296 LINDOGlobal SOLVER USECUTOFFVAL
Page 298 and 299: 298 LINDOGlobal 0 Solver decides 1
Page 300 and 301: 300 LINDOGlobal MIP INTTOL (real) A
Page 302 and 303: 302 LINDOGlobal MIP HEULEVEL (integ
Page 304 and 305: 304 LINDOGlobal MIP BRANCH PRIO (in
Page 306 and 307: 306 LINDOGlobal 1 Base MIP calculat
Page 308 and 309: 308 LINDOGlobal POSTLEVEL (integer)
Page 310 and 311: 310 LINDOGlobal
Page 312 and 313: 312 LogMIP
Page 314 and 315: 314 MILES When l = −∞ and u =
Page 316 and 317: 316 MILES Given z, MILES uses the v
Page 318 and 319: 318 MILES Pivoting Rules When z 0 e
Page 320 and 321: 320 MILES Pivot Selection Option De
Page 324 and 325: 324 MILES INFEAS. PIVOTS IN/OUT is
Page 326 and 327: 326 MILES Table 4 Status File with
Page 328 and 329: 328 MILES Table 6 Status File with
Page 330 and 331: 330 MILES N.H. Josephy, ”Newton
Page 332 and 333: 332 MILES Table 8 Transport Model i
Page 334 and 335: 334 MINOS 1 Introduction This docum
Page 336 and 337: 336 MINOS their bounds: l j − δ
Page 338 and 339: 338 MINOS 4 Modeling Issues Formula
Page 340 and 341: 340 MINOS obj.. z =e= sum(i, sqr(re
Page 342 and 343: 342 MINOS reform This option will i
Page 344 and 345: 344 MINOS 6.5 Examples of GAMS/MINO
Page 346 and 347: 346 MINOS B. A. Murtagh, University
Page 348 and 349: 348 MINOS MINOS-Link May 25, 2002 W
Page 350 and 351: 350 MINOS crash option 2 Only the c
Page 352 and 353: 352 MINOS The storage required if o
Page 354 and 355: 354 MINOS linear variables y or the
Page 356 and 357: 356 MINOS Pivot Tolerance r Broadly
Page 358 and 359: 358 MINOS Solution yes Solution no
Page 360 and 361: 360 MINOS Verify option 3 A detaile
Page 362 and 363: 362 MINOS The simple way to solve t
Page 364 and 365: 364 MINOS REFERENCES
Page 366 and 367: 366 MOSEK Furthermore, MOSEK can so
Page 368 and 369: 368 MOSEK 1.5 Nonlinear Programs MO
Page 370 and 371: 370 MOSEK The original problem is:
Page 372 and 373:
372 MOSEK The first option specifie
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374 MOSEK MSK IPAR LOG BI output co
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376 MOSEK MSK IPAR SIM PRIMAL CRASH
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378 MOSEK MSK IPAR PRESOLVE LINDEP
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380 MOSEK MSK DPAR DATA TOL QIJ (re
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382 MOSEK MSK DPAR INTPNT CO TOL NE
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384 MOSEK MSK IPAR INTPNT STARTING
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386 MOSEK MSK IPAR SIM PRIMAL CRASH
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388 MOSEK Coefficient reduction +51
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390 MOSEK 8 The optimizer for nonco
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392 MOSEK Simplex - cpu time: 0.00
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394 MOSEK Presolve - time : 0.00 Pr
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396 MPSWRITE need to use applicatio
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398 MPSWRITE C0000004 X SAN-DIEGO N
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400 MPSWRITE 6 Using Analyze with M
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402 MPSWRITE 7 The GAMS/MPSWRITE Op
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404 MPSWRITE 8 Name Generation Exam
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406 MPSWRITE C CHICAGO T TOPEKA I c
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408 MPSWRITE the macros @i and @j.
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410 MPSWRITE SSA 3 -0.10000000E+21
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412 MPSWRITE < translate .lp file i
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414 MPSWRITE ANALYZE Version 10.0 b
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416 NLPEC gams nash MPEC=nlpec MCP=
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418 NLPEC Note that each inner prod
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420 NLPEC Note that the slack varia
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422 NLPEC 3.2.1 Doubly bounded vari
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424 NLPEC Option Description Defaul
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426 NLPEC L/U B equref reftype sign
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428 NLPEC
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430 OQNLP and MSNLP the set gathere
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432 OQNLP and MSNLP Itn Penval Meri
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434 OQNLP and MSNLP this guide. You
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436 OQNLP and MSNLP Option Descript
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438 OQNLP and MSNLP ENDDO xt ∗ =
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440 OQNLP and MSNLP Return xt This
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442 OSL 3 Overview of OSL OSL offer
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444 OSL sets the amount of memory u
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446 OSL 5.5 Examples of GAMS/OSL Op
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448 OSL Option Description Default
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450 OSL Option Description Default
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452 OSL 7 Special Notes This sectio
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454 OSL 9 Examples of MPS Files Wri
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456 OSL XU C0000004 R0000004 0.0000
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458 OSL Stochastic Extensions The s
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460 OSL Stochastic Extensions 4.2 M
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462 OSL Stochastic Extensions Optio
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464 OSL Stochastic Extensions
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466 PATH 4.6 3.3 Difficult Models .
Page 468 and 469:
468 PATH 4.6 sets i canning plants,
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470 PATH 4.6 $include walras.dat po
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472 PATH 4.6 An advantage of the ex
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474 PATH 4.6 S O L V E S U M M A R
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476 PATH 4.6 which has a unique sol
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478 PATH 4.6 --- Starting compilati
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480 PATH 4.6 Code Meaning C A cycle
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482 PATH 4.6 At the end of the log
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484 PATH 4.6 Option Default Explana
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486 PATH 4.6 2.6 Preprocessing The
Page 488 and 489:
488 PATH 4.6 In the context of nonl
Page 490 and 491:
490 PATH 4.6 the generated path ema
Page 492 and 493:
492 PATH 4.6 Figure 28.10: Merit Fu
Page 494 and 495:
494 PATH 4.6 INITIAL POINT STATISTI
Page 496 and 497:
496 PATH 4.6 A.1 Classical Model Th
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498 PATH 4.6 7 orders of magnitude
Page 500 and 501:
PATH References [1] S. C. Billups.
Page 502 and 503:
502 PATH REFERENCES
Page 504 and 505:
504 PATHNLP The standard GAMS model
Page 506 and 507:
506 SBB • March 21, 2001: Level 0
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508 SBB Option Description Default
Page 510 and 511:
510 SBB Solution satisfies optcr St
Page 512 and 513:
512 SBB Non convex model! # jumps i
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514 SCENRED running time) of the me
Page 516 and 517:
516 SCENRED eter stored in the SCEN
Page 518 and 519:
518 SCENRED 6 The SCENRED Output Fi
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520 SCENRED 9 SCENRED Warnings SCEN
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522 SNOPT to be stated in the form
Page 524 and 525:
524 SNOPT 2.2 Constraints and slack
Page 526 and 527:
526 SNOPT By analogy with the eleme
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528 SNOPT * fill with random data x
Page 530 and 531:
530 SNOPT 4 Options In many cases N
Page 532 and 533:
532 SNOPT of (nonlinear) nonzeroes,
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534 SNOPT In all cases, a derivativ
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536 SNOPT • t must be a real valu
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538 SNOPT s a single line that give
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540 SNOPT • It is common for two
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542 SNOPT Unbounded objective value
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544 SNOPT --- Starting execution --
Page 546 and 547:
546 SNOPT Merit is the value of the
Page 548 and 549:
548 SNOPT EXIT -- Requested accurac
Page 550 and 551:
550 SNOPT EXIT -- Function evaluati
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552 SNOPT The possible EXIT message
Page 554 and 555:
554 PATH REFERENCES
Page 556 and 557:
556 XA during the course of program
Page 558 and 559:
558 XA Each XA B&B strategy has man
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560 XA Option Description Default D
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562 XA Option Description Default S
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564 XA
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566 XPRESS • option iterlim=n; or
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568 XPRESS Option Description Defau
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Page 572 and 573:
Page 574:
574 XPRESS
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