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284 LGO Illustrative References R. Horst and P. M. Pardalos, Editors (1995) Handbook of Global Optimization. Vol. 1. Kluwer Academic Publishers, Dordrecht. P. M. Pardalos and H. E. Romeijn, Editors (2002) Handbook of Global Optimization. Vol. 2. Kluwer Academic Publishers, Dordrecht. J. D. Pintér (1996) Global Optimization in Action, Kluwer Academic Publishers, Dordrecht. J. D. Pintér (2001) Computational Global Optimization in Nonlinear Systems: An Interactive Tutorial, Lionheart Publishing, Atlanta, GA. J. D. Pintér (2002) Global optimization: software, tests and applications. Chapter 15 (pp. 515-569) in: Pardalos and Romeijn, Editors, Handbook of Global Optimization. Vol. 2. Kluwer Academic Publishers, Dordrecht.
LINDOGlobal Lindo Systems, Inc. Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 1.1 Licensing and software requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 1.2 Running GAMS/LINDOGlobal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 2 Supported nonlinear functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286 3 GAMS/LINDOGlobal output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 4 Summary of LINDOGlobal Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 4.1 LINDOGlobal Options File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 4.2 General Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 4.3 LP Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 4.4 MIP Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 4.5 NLP Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 4.6 Global Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292 5 Detailed Descriptions of LINDOGLOBAL Options . . . . . . . . . . . . . . . . . . . 293 1 Introduction GAMS/LINDOGlobal finds guaranteed globally optimal solutions to general nonlinear problems with continuous and/or discrete variables. GAMS/LINDOGlobal supports most mathematical functions, including functions that are nonsmooth, such as abs(x) and or even discontinuous, such as floor(x). Nonlinear solvers employing methods like successive linear programming (SLP) or generalized reduced gradient (GRG) return a local optimal solution to an NLP problem. However, many practical nonlinear models are non-convex and have more than one local optimal solution. In some applications, the user may want to find a global optimal solution. The LINDO global optimization procedure(GOP) employs branch-and-cut methods to break an NLP model down into a list of subproblems. Each subproblem is analyzed and either a) is shown to not have a feasible or optimal solution, or b) an optimal solution to the subproblem is found, e.g., because the subproblem is shown to be convex, or c) the subproblem is further split into two or more subproblems which are then placed on the list. Given appropriate tolerances, after a finite, though possibly large number of steps a solution provably global optimal to tolerances is returned. Traditional nonlinear solvers can get stuck at suboptimal, local solutions. This is no longer the case when using the global solver. GAMS/LINDOGlobal can automatically linearize a number of nonlinear relationships, such as max(x,y), through the addition of constraints and integer variables, so the transformed linearized model is mathematically equivalent to the original nonlinear model. Keep in mind, however, that each of these strategies will require additional computation time. Thus, formulating models, so they are convex and contain a single extremum, is desirable. In order to decrease required computing power and time it is also possible to disable the global solver and use GAMS/LINDOGlobal like a regular nonlinear solver. GAMS/LINDOGlobal has a multistart feature that restarts the standard (non-global) nonlinear solver from a number of intelligently generated points. This allows the solver to find a number of locally optimal points and
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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
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
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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
Page 234 and 235: 234 DICOPT Although the algorithm h
Page 236 and 237: 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
Page 242 and 243: 242 DICOPT * stop only on infeasibl
Page 244 and 245: 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
Page 254 and 255: 254 DICOPT REFERENCES
Page 256 and 257: 256 EMP
Page 258 and 259: 258 EXAMINER The optimality checks
Page 260 and 261: 260 EXAMINER Option Description Def
Page 262 and 263: 262 EXAMINER
Page 264 and 265: 264 GAMS/AMPL --- No AmplPath optio
Page 266 and 267: 266 GAMS/LINGO --- No LingoPath opt
Page 268 and 269: 268 KNITRO • Derivative-free, 1st
Page 270 and 271: 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 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 322 and 323: 322 MILES Table 2 Sample Iteration
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
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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
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340 MINOS obj.. z =e= sum(i, sqr(re
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342 MINOS reform This option will i
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344 MINOS 6.5 Examples of GAMS/MINO
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346 MINOS B. A. Murtagh, University
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348 MINOS MINOS-Link May 25, 2002 W
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350 MINOS crash option 2 Only the c
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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
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360 MINOS Verify option 3 A detaile
Page 362 and 363:
362 MINOS The simple way to solve t
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364 MINOS REFERENCES
Page 366 and 367:
366 MOSEK Furthermore, MOSEK can so
Page 368 and 369:
368 MOSEK 1.5 Nonlinear Programs MO
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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
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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
Page 398 and 399:
398 MPSWRITE C0000004 X SAN-DIEGO N
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400 MPSWRITE 6 Using Analyze with M
Page 402 and 403:
402 MPSWRITE 7 The GAMS/MPSWRITE Op
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404 MPSWRITE 8 Name Generation Exam
Page 406 and 407:
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
Page 414 and 415:
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
Page 422 and 423:
422 NLPEC 3.2.1 Doubly bounded vari
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424 NLPEC Option Description Defaul
Page 426 and 427:
426 NLPEC L/U B equref reftype sign
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428 NLPEC
Page 430 and 431:
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
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
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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
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
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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
Page 484 and 485:
484 PATH 4.6 Option Default Explana
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486 PATH 4.6 2.6 Preprocessing The
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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
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496 PATH 4.6 A.1 Classical Model Th
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498 PATH 4.6 7 orders of magnitude
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PATH References [1] S. C. Billups.
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502 PATH REFERENCES
Page 504 and 505:
504 PATHNLP The standard GAMS model
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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
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,
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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
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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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