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464 OSL Stochastic Extensions
PATH 4.6 Michael C. Ferris Todd S. Munson Contents 1 Complementarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 1.1 Transportation Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466 1.1.1 <strong>GAMS</strong> Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 1.1.2 Extension: Model Generalization . . . . . . . . . . . . . . . . . . . . . . . . . . 469 1.1.3 Nonlinear Complementarity Problem . . . . . . . . . . . . . . . . . . . . . . . 469 1.2 Walrasian Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 1.2.1 <strong>GAMS</strong> Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 1.2.2 Extension: Intermediate Variables . . . . . . . . . . . . . . . . . . . . . . . . . 470 1.2.3 Mixed Complementarity Problem . . . . . . . . . . . . . . . . . . . . . . . . . 471 1.3 Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472 1.3.1 Listing File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 1.3.2 Redefined Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 1.4 Pitfalls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 2 PATH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 2.1 Log File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 2.1.1 Diagnostic Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 2.1.2 Crash Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 2.1.3 Major Iteration Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 2.1.4 Minor Iteration Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 2.1.5 Restart Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 2.1.6 Solution Log . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481 2.2 Status File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 2.3 User Interrupts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 2.4 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482 2.5 PATHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 2.6 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 2.6.1 Constrained Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 3 Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 3.1 Formal Definition of MCP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 3.2 Algorithmic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 3.2.1 Merit Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487 3.2.2 Crashing Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 3.2.3 Nonmontone Searches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488 3.2.4 Linear Complementarity Problems . . . . . . . . . . . . . . . . . . . . . . . . . 489 3.2.5 Other Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
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GAMS — The Solver Manuals c○ 20
Page 4 and 5:
4 CONTENTS
Page 6 and 7:
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
Page 44 and 45:
44 BENCH To terminate not only the
Page 46 and 47:
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
Page 52 and 53:
52 COIN-OR Option type default B-BB
Page 54 and 55:
54 COIN-OR integer tolerance: Set i
Page 56 and 57:
56 COIN-OR stop diving on cutoff: F
Page 58 and 59:
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
Page 64 and 65:
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
Page 88 and 89:
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+
Page 116 and 117:
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
Page 164 and 165:
164 CPLEX 11 • You can collect al
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166 CPLEX 11 individual GDX solutio
Page 168 and 169:
168 CPLEX 11 parallelmode predual p
Page 170 and 171:
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
Page 180 and 181:
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
Page 238 and 239:
238 DICOPT option rminlp=minos; sol
Page 240 and 241:
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 . . .
Page 246 and 247:
246 DICOPT nlptracelevel 3 As nlptr
Page 248 and 249:
248 DICOPT --- DICOPT: Checking con
Page 250 and 251:
250 DICOPT NLP 2 1.72097< 0.00 3 0
Page 252 and 253:
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
Page 262 and 263:
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
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272 KNITRO Option Description Defau
Page 274 and 275:
274 KNITRO If outlev=2, information
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276 KNITRO (Dense) Quasi-Newton BFG
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KNITRO References [1] R. H. Byrd, J
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280 LGO GAMS/LGO does not rely on a
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282 LGO 3 The GAMS/LGO Log File The
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284 LGO Illustrative References R.
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286 LINDOGlobal report the best one
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288 LINDOGlobal Infeasibility of be
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290 LINDOGlobal MIP AOPTTIMLIM time
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292 LINDOGlobal 4.5 NLP Options NLP
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294 LINDOGlobal 3 Decomposed model
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296 LINDOGlobal SOLVER USECUTOFFVAL
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298 LINDOGlobal 0 Solver decides 1
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300 LINDOGlobal MIP INTTOL (real) A
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302 LINDOGlobal MIP HEULEVEL (integ
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304 LINDOGlobal MIP BRANCH PRIO (in
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306 LINDOGlobal 1 Base MIP calculat
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308 LINDOGlobal POSTLEVEL (integer)
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310 LINDOGlobal
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312 LogMIP
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314 MILES When l = −∞ and u =
Page 316 and 317:
316 MILES Given z, MILES uses the v
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318 MILES Pivoting Rules When z 0 e
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320 MILES Pivot Selection Option De
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322 MILES Table 2 Sample Iteration
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324 MILES INFEAS. PIVOTS IN/OUT is
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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
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332 MILES Table 8 Transport Model i
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334 MINOS 1 Introduction This docum
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336 MINOS their bounds: l j − δ
Page 338 and 339:
338 MINOS 4 Modeling Issues Formula
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340 MINOS obj.. z =e= sum(i, sqr(re
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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
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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
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356 MINOS Pivot Tolerance r Broadly
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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
Page 374 and 375:
374 MOSEK MSK IPAR LOG BI output co
Page 376 and 377:
376 MOSEK MSK IPAR SIM PRIMAL CRASH
Page 378 and 379:
378 MOSEK MSK IPAR PRESOLVE LINDEP
Page 380 and 381:
380 MOSEK MSK DPAR DATA TOL QIJ (re
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382 MOSEK MSK DPAR INTPNT CO TOL NE
Page 384 and 385:
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
Page 396 and 397:
396 MPSWRITE need to use applicatio
Page 398 and 399:
398 MPSWRITE C0000004 X SAN-DIEGO N
Page 400 and 401:
400 MPSWRITE 6 Using Analyze with M
Page 402 and 403:
402 MPSWRITE 7 The GAMS/MPSWRITE Op
Page 404 and 405:
404 MPSWRITE 8 Name Generation Exam
Page 406 and 407:
406 MPSWRITE C CHICAGO T TOPEKA I c
Page 408 and 409:
408 MPSWRITE the macros @i and @j.
Page 410 and 411:
410 MPSWRITE SSA 3 -0.10000000E+21
Page 412 and 413:
412 MPSWRITE < translate .lp file i
Page 414 and 415: 414 MPSWRITE ANALYZE Version 10.0 b
Page 416 and 417: 416 NLPEC gams nash MPEC=nlpec MCP=
Page 418 and 419: 418 NLPEC Note that each inner prod
Page 420 and 421: 420 NLPEC Note that the slack varia
Page 422 and 423: 422 NLPEC 3.2.1 Doubly bounded vari
Page 424 and 425: 424 NLPEC Option Description Defaul
Page 426 and 427: 426 NLPEC L/U B equref reftype sign
Page 428 and 429: 428 NLPEC
Page 430 and 431: 430 OQNLP and MSNLP the set gathere
Page 432 and 433: 432 OQNLP and MSNLP Itn Penval Meri
Page 434 and 435: 434 OQNLP and MSNLP this guide. You
Page 436 and 437: 436 OQNLP and MSNLP Option Descript
Page 438 and 439: 438 OQNLP and MSNLP ENDDO xt ∗ =
Page 440 and 441: 440 OQNLP and MSNLP Return xt This
Page 442 and 443: 442 OSL 3 Overview of OSL OSL offer
Page 444 and 445: 444 OSL sets the amount of memory u
Page 446 and 447: 446 OSL 5.5 Examples of GAMS/OSL Op
Page 448 and 449: 448 OSL Option Description Default
Page 450 and 451: 450 OSL Option Description Default
Page 452 and 453: 452 OSL 7 Special Notes This sectio
Page 454 and 455: 454 OSL 9 Examples of MPS Files Wri
Page 456 and 457: 456 OSL XU C0000004 R0000004 0.0000
Page 458 and 459: 458 OSL Stochastic Extensions The s
Page 460 and 461: 460 OSL Stochastic Extensions 4.2 M
Page 462 and 463: 462 OSL Stochastic Extensions Optio
Page 466 and 467: 466 PATH 4.6 3.3 Difficult Models .
Page 468 and 469: 468 PATH 4.6 sets i canning plants,
Page 470 and 471: 470 PATH 4.6 $include walras.dat po
Page 472 and 473: 472 PATH 4.6 An advantage of the ex
Page 474 and 475: 474 PATH 4.6 S O L V E S U M M A R
Page 476 and 477: 476 PATH 4.6 which has a unique sol
Page 478 and 479: 478 PATH 4.6 --- Starting compilati
Page 480 and 481: 480 PATH 4.6 Code Meaning C A cycle
Page 482 and 483: 482 PATH 4.6 At the end of the log
Page 484 and 485: 484 PATH 4.6 Option Default Explana
Page 486 and 487: 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
Page 498 and 499: 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
Page 508 and 509: 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
Page 514 and 515:
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
Page 520 and 521:
520 SCENRED 9 SCENRED Warnings SCEN
Page 522 and 523:
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
Page 528 and 529:
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,
Page 534 and 535:
534 SNOPT In all cases, a derivativ
Page 536 and 537:
536 SNOPT • t must be a real valu
Page 538 and 539:
538 SNOPT s a single line that give
Page 540 and 541:
540 SNOPT • It is common for two
Page 542 and 543:
542 SNOPT Unbounded objective value
Page 544 and 545:
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
Page 552 and 553:
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
Page 560 and 561:
560 XA Option Description Default D
Page 562 and 563:
562 XA Option Description Default S
Page 564 and 565:
564 XA
Page 566 and 567:
566 XPRESS • option iterlim=n; or
Page 568 and 569:
568 XPRESS Option Description Defau
Page 570 and 571:
Page 572 and 573:
Page 574:
574 XPRESS
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