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18 AlphaECP Westerlund T. and Pettersson F. (1995). An Extended Cutting Plane Method for Solving Convex MINLP Problems. Computers Chem. Engng Sup., 19, 131-136. Westerlund T., Skrifvars H., Harjunkoski I. and Pörn R. (1998). An Extended Cutting Plane Method for Solving a Class of Non-Convex MINLP Problems. Computers Chem. Engng, 22, 357-365. Westerlund T. and Pörn R. (2002). Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques. Optimization and Engineering, 3, 253-280.
BARON Nick Sahinidis; University of Illinois at Urbana-Champaign, Department of Chemical and Biomolecular Engineering, 600 South Mathews Avenue, Urbana, IL 61801, nikos@uiuc.edu Mohit Tawarmalani; Purdue University, Krannert School of Management, West Lafayette, IN 47907, mtawarma@mgmt.purdue.edu Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.1 Licensing and software requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2 Running GAMS/BARON . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Model requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1 Variable and expression bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.2 Allowable nonlinear functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3 BARON output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.1 BARON log output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Termination messages, model and solver statuses . . . . . . . . . . . . . . . . . . . . . . 22 4 Some BARON features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1 No starting point is required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 Finding the best, second best, third best, etc. solution, or all feasible solutions . . . . . 24 4.3 Using BARON as a multi-start heuristic solver . . . . . . . . . . . . . . . . . . . . . . . 25 5 The BARON options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.1 Setting variable bounds and branching priorities . . . . . . . . . . . . . . . . . . . . . . 25 5.2 Termination options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.3 Relaxation options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.4 Range reduction options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 5.5 Branching options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.6 Heuristic local search options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.7 Output options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.8 Other options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 1 Introduction The Branch-And-Reduce Optimization Navigator (BARON) is a GAMS solver for the global solution of nonlinear (NLP) and mixed-integer nonlinear programs (MINLP). While traditional NLP and MINLP algorithms are guaranteed to converge only under certain convexity assumptions, BARON implements deterministic global optimization algorithms of the branch-and-bound type that are guaranteed to provide global optima under fairly general assumptions. These include the availability of finite lower and upper bounds on the variables and their expressions in the NLP or MINLP to be solved. BARON implements algorithms of the branch-and-bound type enhanced with a variety of constraint propagation and duality techniques for reducing ranges of variables in the course of the algorithm.
Page 1: GAMS — The Solver Manuals c○ 20
Page 4 and 5: 4 CONTENTS
Page 6 and 7: 6 Basic Solver Usage Option iterlim
Page 8 and 9: 8 Basic Solver Usage keyword(s) [mo
Page 10 and 11: 10 AlphaECP 1.2 Running GAMS/AlphaE
Page 12 and 13: 12 AlphaECP A: Infeasible, deleted
Page 14 and 15: 14 AlphaECP 0 Never. 1 Call the NLP
Page 16 and 17: 16 AlphaECP mipoptcr (real) Relativ
Page 20 and 21: 20 BARON 1.1 Licensing and software
Page 22 and 23: 22 BARON on probing : 000:00:00, in
Page 24 and 25: 24 BARON 4.2 Finding the best, seco
Page 26 and 27: 26 BARON in the form of solver boun
Page 28 and 29: 28 BARON 5.4 Range reduction option
Page 30 and 31: 30 BARON 5.6 Heuristic local search
Page 32 and 33: 32 BARON Option Description Default
Page 34 and 35: 34 BDMLP
Page 36 and 37: 36 BENCH option modeltype=bench; Th
Page 38 and 39: 38 BENCH Option Description Default
Page 40 and 41: 40 BENCH In the example below, EXAM
Page 42 and 43: 42 BENCH --- Spawning solver : CPLE
Page 44 and 45: 44 BENCH To terminate not only the
Page 46 and 47: 46 BENCH
Page 48 and 49: 48 COIN-OR also found their way int
Page 50 and 51: 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
Page 60 and 61: 60 COIN-OR nlp solve max depth: Set
Page 62 and 63: 62 COIN-OR maxmin crit no sol: Weig
Page 64 and 65: 64 COIN-OR General Options iterlim
Page 66 and 67: 66 COIN-OR This option causes GAMS
Page 68 and 69:
68 COIN-OR scaling (string) Scaling
Page 70 and 71:
70 COIN-OR sos This option let CBC
Page 72 and 73:
72 COIN-OR knapsackcuts (string) De
Page 74 and 75:
74 COIN-OR 1 Turns the feasibility
Page 76 and 77:
76 COIN-OR userheurmult (integer) D
Page 78 and 79:
78 COIN-OR This option determines t
Page 80 and 81:
80 COIN-OR noiterlim (integer) Allo
Page 82 and 83:
82 COIN-OR linear_solver pardiso pa
Page 84 and 85:
84 COIN-OR # This is a comment # Tu
Page 86 and 87:
86 COIN-OR acceptable tol: ”Accep
Page 88 and 89:
88 COIN-OR slack bound push: Desire
Page 90 and 91:
90 COIN-OR linear system scaling: M
Page 92 and 93:
92 COIN-OR mumps pivtol: Pivot tole
Page 94 and 95:
94 COIN-OR fixed variable treatment
Page 96 and 97:
96 COIN-OR adaptive mu monotone ini
Page 98 and 99:
98 COIN-OR quality function balanci
Page 100 and 101:
100 COIN-OR alpha min frac: Safety
Page 102 and 103:
102 COIN-OR • no: don’t skip
Page 104 and 105:
104 COIN-OR max resto iter: Maximum
Page 106 and 107:
106 COIN-OR • no: perturbation on
Page 108 and 109:
108 COIN-OR 6.2 Usage of CoinScip T
Page 110 and 111:
110 COIN-OR gams/usergdxname (strin
Page 112 and 113:
112 CONOPT 1 Introduction Nonlinear
Page 114 and 115:
114 CONOPT 130 0 103 2.1776589484E+
Page 116 and 117:
116 CONOPT The two messages above t
Page 118 and 119:
118 CONOPT CONOPT time Total 0.109
Page 120 and 121:
120 CONOPT 6 Hints on Good Model Fo
Page 122 and 123:
122 CONOPT by the reduced complexit
Page 124 and 125:
124 CONOPT of 4.1**2, which means t
Page 126 and 127:
126 CONOPT X.SCALE(I,J,K)$IJK(I,J,K
Page 128 and 129:
128 CONOPT delta. The error is redu
Page 130 and 131:
130 CONOPT the NLP solver will comp
Page 132 and 133:
132 CONOPT The relationship between
Page 134 and 135:
134 CONOPT A : ❅ ❅ ❅ ❅ Zero
Page 136 and 137:
136 CONOPT EQUATION E1, E2, E3, E4;
Page 138 and 139:
138 CONOPT unfortunate that a redun
Page 140 and 141:
140 CONOPT The Crash procedure is n
Page 142 and 143:
142 CONOPT infeasible equations (th
Page 144 and 145:
144 CONOPT The steepest edge proced
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146 CONOPT CONOPT will after the pr
Page 148 and 149:
148 CONOPT X2 appearing in E2: Pivo
Page 150 and 151:
150 CONOPT Until a final solution h
Page 152 and 153:
152 CONOPT Option Description Defau
Page 154 and 155:
154 CONOPT Option Description Defau
Page 156 and 157:
156 CONOPT
Page 158 and 159:
158 CONVERT • LindoMPI • LINGO
Page 160 and 161:
160 CONVERT Option Description Defa
Page 162 and 163:
162 CPLEX 11 2 How to Run a Model w
Page 164 and 165:
164 CPLEX 11 • You can collect al
Page 166 and 167:
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
Page 172 and 173:
172 CPLEX 11 6 Special Notes 6.1 Ph
Page 174 and 175:
174 CPLEX 11 Start. The number of t
Page 176 and 177:
176 CPLEX 11 Aggregator did 30 subs
Page 178 and 179:
178 CPLEX 11 Nodes Cuts/ Node Left
Page 180 and 181:
180 CPLEX 11 baritlim (integer) Det
Page 182 and 183:
182 CPLEX 11 -1 Do not generate cov
Page 184 and 185:
184 CPLEX 11 .divflt (real) A diver
Page 186 and 187:
186 CPLEX 11 feasoptmode (integer)
Page 188 and 189:
188 CPLEX 11 implbd (integer) Deter
Page 190 and 191:
190 CPLEX 11 wasted computation tim
Page 192 and 193:
192 CPLEX 11 netppriind (integer) N
Page 194 and 195:
194 CPLEX 11 Settings of this paral
Page 196 and 197:
196 CPLEX 11 1 Force node presolve
Page 198 and 199:
198 CPLEX 11 repairtries (integer)
Page 200 and 201:
200 CPLEX 11 simdisplay (integer) T
Page 202 and 203:
202 CPLEX 11 populate procedure aga
Page 204 and 205:
204 CPLEX 11 1 Display standard min
Page 206 and 207:
206 CPLEX 11
Page 208 and 209:
208 DECIS 1 DECIS 1.1 Introduction
Page 210 and 211:
210 DECIS 1.4 Solving the Universe
Page 212 and 213:
212 DECIS SMPS (stochastic mathemat
Page 214 and 215:
214 DECIS statement would work as w
Page 216 and 217:
216 DECIS RHS demand m 1000.00 peri
Page 218 and 219:
218 DECIS omega1 defines all realiz
Page 220 and 221:
220 DECIS nzrows — Number of rows
Page 222 and 223:
222 DECIS Example The following exa
Page 224 and 225:
224 DECIS 20 0.2464E+05 0.2464E+05
Page 226 and 227:
226 DECIS pro 0.1 0.2 0.5 0.1 0.1 ;
Page 228 and 229:
228 DECIS parameter hm2(dl) / h 100
Page 230 and 231:
230 DECIS 15. ERROR: error code: in
Page 232 and 233:
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 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 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
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
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
Page 382 and 383:
382 MOSEK MSK DPAR INTPNT CO TOL NE
Page 384 and 385:
384 MOSEK MSK IPAR INTPNT STARTING
Page 386 and 387:
386 MOSEK MSK IPAR SIM PRIMAL CRASH
Page 388 and 389:
388 MOSEK Coefficient reduction +51
Page 390 and 391:
390 MOSEK 8 The optimizer for nonco
Page 392 and 393:
392 MOSEK Simplex - cpu time: 0.00
Page 394 and 395:
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 464 and 465:
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
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
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478 PATH 4.6 --- Starting compilati
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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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