What Is Optimization Toolbox?

More documents

Recommendations

Info

$Producing Beautiful Documents With TEX and LATEX$

fminunc[3] Coleman, T.F. and Y. Li, “On the Convergence of Reflective NewtonMethods for Large-Scale Nonlinear Minimization Subject to Bounds,”Mathematical Programming, Vol. 67, Number 2, pp. 189-224, 1994.[4] Davidon, W.C., “Variable Metric Method for Minimization,” A.E.C.Research and Development Report, ANL-5990, 1959.[5] Fletcher, R., “A New Approach to Variable Metric Algorithms,”Computer Journal, Vol. 13, pp. 317-322, 1970.[6] Fletcher, R., “Practical Methods of <strong>Optimization</strong>,” Vol. 1,Unconstrained <strong>Optimization</strong>, John Wiley and Sons, 1980.[7] Fletcher, R. and M.J.D. Powell, “A Rapidly Convergent DescentMethod for Minimization,” Computer Journal, Vol. 6, pp. 163-168, 1963.[8] Goldfarb, D., “A Family of Variable Metric Updates Derived byVariational Means,” Mathematics of Computing, Vol. 24, pp. 23-26,1970.[9] Shanno, D.F., “Conditioning of Quasi-Newton Methods for FunctionMinimization,” Mathematics of Computing, Vol. 24, pp. 647-656, 1970.See Also@ (function_handle), fminsearch, optimset, optimtool, anonymousfunctions8-90
fseminfPurposeEquationFind minimum of semi-infinitely constrained multivariable nonlinearfunctionFinds the minimum of a problem specified bywhere x, b, beq, lb, andub are vectors, A and Aeq are matrices, c(x),ceq(x), and K i(x,wi) are functions that return vectors, and f(x) isafunction that returns a scalar. f(x), c(x), and ceq(x) can be nonlinearfunctions. The vectors (or matrices)are continuousfunctions of both x and an additional set of variables.Thevariablesare vectors of, at most, length two.Syntaxx = fseminf(fun,x0,ntheta,seminfcon)x = fseminf(fun,x0,ntheta,seminfcon,A,b)x = fseminf(fun,x0,ntheta,seminfcon,A,b,Aeq,beq)x = fseminf(fun,x0,ntheta,seminfcon,A,b,Aeq,beq,lb,ub)x = fseminf(fun,x0,ntheta,seminfcon,A,b,Aeq,beq,lb,ub,options)[x,fval] = fseminf(...)[x,fval,exitflag] = fseminf(...)[x,fval,exitflag,output] = fseminf(...)[x,fval,exitflag,output,lambda] = fseminf(...)8-91
Page 1 and 2:
Optimization Toolbox 3User’s Guid
Page 3:
Revision HistoryNovember 1990 First
Page 6 and 7:
Acknowledgments
Page 8 and 9:
Nonlinear Equations with Finite-Dif
Page 10 and 11:
Quadratic Programming (QP) Subprobl
Page 12 and 13:
Specifying the Options ............
Page 14 and 15:
xivContents
Page 16 and 17:
1 Getting StartedWhat Is Optimizati
Page 18 and 19:
1 Getting StartedOptimization Examp
Page 20 and 21:
1 Getting Started[x, fval] =lsqlin(
Page 22 and 23:
2 TutorialLarge-Scale Examples (p.
Page 24 and 25:
2 TutorialMinimization (Continued)T
Page 26 and 27:
2 TutorialUsing the Optimization Fu
Page 28 and 29:
2 TutorialA choice of line search s
Page 30 and 31:
2 TutorialThe tutorial uses the fun
Page 32 and 33:
2 Tutorialfunction evaluations. See
Page 34 and 35:
2 TutorialTo restrict x inEquation2
Page 36 and 37:
2 Tutorialceq=[];DCeq = [ ];G conta
Page 38 and 39:
2 TutorialEquality Constrained Exam
Page 40 and 41:
2 Tutorialfunction y = findzero(b,
Page 42 and 43:
2 Tutorial3.7081Sharing Variables U
Page 44 and 45:
2 Tutorialcomponents.');end% Evalua
Page 46 and 47:
2 TutorialThe example produces the
Page 48 and 49:
2 TutorialClosed-Loop ResponseThe p
Page 50 and 51:
2 Tutorialfunction [Kp,Ki,Kd] = run
Page 52 and 53:
2 TutorialThe resulting closed-loop
Page 54 and 55:
2 Tutorialcalling the simulation tw
Page 56 and 57:
2 TutorialThe last value shown in t
Page 58 and 59:
2 TutorialStep 1: Write an M-file f
Page 60 and 61:
2 TutorialLarge-Scale Examples•
Page 62 and 63:
2 TutorialNote The following table
Page 64 and 65:
2 TutorialLarge-Scale Problem Cover
Page 66 and 67:
2 Tutorialoptimset('Display','iter'
Page 68 and 69:
2 Tutorialeither) then, in this pro
Page 70 and 71:
2 TutorialNonlinear Least-Squares w
Page 72:
2 TutorialThe problem is to find x
Page 75 and 76:
Large-Scale Examplesto zero (for fm
Page 77 and 78:
Large-Scale Examples024681012141618
Page 79 and 80:
Large-Scale Examplesfval =270.4790o
Page 81 and 82:
Large-Scale Examplesans =1.1885e-01
Page 83 and 84:
Large-Scale ExamplesW = Hinfo*Y - V
Page 85 and 86:
Large-Scale Exampleswere not the sa
Page 87 and 88:
Large-Scale Examplestradeoff is ben
Page 89 and 90:
Large-Scale Examplesfunction W = qp
Page 91 and 92:
Large-Scale Examples% RUNQPBOX4PREC
Page 93 and 94:
Large-Scale Examplesalgorithm: 'lar
Page 95 and 96:
Large-Scale Examplescgiterations: 0
Page 97 and 98:
Large-Scale Examplesdoes not give a
Page 99 and 100:
Default Options SettingsDetermining
Page 101 and 102:
Displaying Iterative OutputDisplayi
Page 103 and 104:
Displaying Iterative Outputbintprog
Page 105 and 106:
Displaying Iterative OutputfsolveTh
Page 107 and 108:
Displaying Iterative Outputlsqnonli
Page 109 and 110:
Calling an Output Function Iterativ
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Optimizing Anonymous Functions Inst
Page 117 and 118:
Optimizing Anonymous Functions Inst
Page 119 and 120:
Typical Problems and How to Deal wi
Page 121 and 122:
Typical Problems and How to Deal wi
Page 123 and 124:
3Standard AlgorithmsStandard Algori
Page 125 and 126:
Multiobjective Optimization (p. 3-4
Page 127 and 128:
Demos of Medium-Scale MethodsDemos
Page 129 and 130:
Unconstrained OptimizationFigure 3-
Page 131 and 132:
Unconstrained Optimizationvariables
Page 133 and 134:
Quasi-Newton ImplementationQuasi-Ne
Page 135 and 136:
Quasi-Newton Implementationvalues o
Page 137 and 138:
Quasi-Newton ImplementationMixed Cu
Page 139 and 140:
Quasi-Newton ImplementationCase 4.3
Page 141 and 142:
Least-Squares OptimizationIn proble
Page 143 and 144:
Least-Squares OptimizationLevenberg
Page 145 and 146:
Least-Squares OptimizationThe linea
Page 147 and 148:
Nonlinear Systems of EquationsNonli
Page 149 and 150:
Nonlinear Systems of Equationsand s
Page 151 and 152:
Constrained OptimizationConstrained
Page 153 and 154:
Constrained OptimizationGiven the p
Page 155 and 156:
Constrained OptimizationUpdating th
Page 157 and 158:
Constrained Optimizationis updated
Page 159 and 160:
Constrained OptimizationInitializat
Page 161 and 162:
Constrained OptimizationSimplex Alg
Page 163 and 164:
Constrained Optimization3 Updates t
Page 165 and 166:
Multiobjective OptimizationMultiobj
Page 167 and 168:
Multiobjective OptimizationIn the t
Page 169 and 170:
Multiobjective OptimizationThe afor
Page 171 and 172:
Multiobjective OptimizationWhat is
Page 173 and 174:
Multiobjective Optimization(3-51)wh
Page 175 and 176:
Selected BibliographySelected Bibli
Page 177 and 178:
Selected Bibliography[24] Han, S.P.
Page 179 and 180:
4Large-Scale AlgorithmsLarge-Scale
Page 181 and 182:
Trust-Region Methods for Nonlinear
Page 183 and 184:
Trust-Region Methods for Nonlinear
Page 185 and 186:
Preconditioned Conjugate GradientsP
Page 187 and 188:
Linearly Constrained ProblemsLinear
Page 189 and 190:
Linearly Constrained ProblemsThe sc
Page 191 and 192:
Quadratic ProgrammingQuadratic Prog
Page 193 and 194:
Large-Scale Linear ProgrammingLarge
Page 195 and 196:
Large-Scale Linear ProgrammingThe a
Page 197 and 198:
Large-Scale Linear ProgrammingWhile
Page 199 and 200:
Selected Bibliography[11] Zhang, Y.
Page 201 and 202:
5Optimization ToolGetting Started w
Page 203 and 204:
Getting Started with the Optimizati
Page 205 and 206:
Selecting a SolverSelecting a Solve
Page 207 and 208:
Defining the ProblemDefining the Pr
Page 209 and 210:
Defining the ProblemFunction to Min
Page 211 and 212:
Defining the ProblemConstraintsLine
Page 213 and 214:
Defining the ProblemM-file, or as a
Page 215 and 216:
Defining the ProblemBounds are lowe
Page 217 and 218:
Defining the Problemfseminf Problem
Page 219 and 220:
Defining the ProblemLinear System o
Page 221 and 222:
Page 223 and 224:
Defining the ProblemConstraintsBoun
Page 225 and 226:
Page 227 and 228:
Defining the ProblemConstraintsWith
Page 229 and 230:
Running a Problem in the Optimizati
Page 231 and 232:
Specifying the Options• Xtoleranc
Page 233 and 234:
Specifying the Optionsoption to a d
Page 235 and 236:
Specifying the OptionsThe following
Page 237 and 238:
Specifying the OptionsMultiobjectiv
Page 239 and 240:
Specifying the OptionsPlot Function
Page 241 and 242:
Specifying the Options• final —
Page 243 and 244:
Importing and Exporting Your WorkIm
Page 245 and 246:
Importing and Exporting Your WorkYo
Page 247 and 248:
Optimization Tool ExamplesOptimizat
Page 249 and 250:
Optimization Tool Examples6 In the
Page 251 and 252:
Optimization Tool Examplesmax Line
Page 253 and 254:
Optimization Tool ExamplesThe Aeq a
Page 255 and 256:
6Argument and OptionsReferenceThis
Page 257 and 258:
Function ArgumentsInput Arguments (
Page 259 and 260:
Function ArgumentsInput Arguments (
Page 261 and 262:
Function ArgumentsOutput Arguments
Page 263 and 264:
Optimization OptionsOptimization Op
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Optimization Optionsspecifies Outpu
Page 273 and 274:
Optimization OptionsoptimValues Fie
Page 275 and 276:
Page 277 and 278:
Page 279 and 280:
Optimization OptionsStopping an Opt
Page 281 and 282:
7Functions — By CategoryMinimizat
Page 283 and 284:
Least Squares (Curve Fitting)Least
Page 285 and 286:
Functions — AlphabeticalList8
Page 287 and 288:
intprogx = bintprog(f,A,b,Aeq,Beq,x
Page 289 and 290:
intprogBranchStrategyStrategy the a
Page 291 and 292:
intprog• Verifies that no better
Page 293 and 294:
intprogExampleTo minimize the funct
Page 295 and 296:
colorPurposeSyntaxDescriptionColumn
Page 297 and 298:
fgoalattainx = fgoalattain(fun,x0,g
Page 299 and 300:
fgoalattainfunThefunctiontobeminimi
Page 301 and 302:
fgoalattainfunction [c,ceq,GC,GCeq]
Page 303 and 304:
fgoalattainattainfactorexitflaglamb
Page 305 and 306:
fgoalattainFunValCheckGoalsExactAch
Page 307 and 308:
fgoalattainExamplesConsider a linea
Page 309 and 310:
fgoalattainof overattainment is met
Page 311 and 312:
fgoalattainLimitationsReferencesThe
Page 313 and 314:
fminbndInputArguments“Function Ar
Page 315 and 316:
fminbndPlotFcnsPlots various measur
Page 317 and 318:
fminbndLimitationsReferencesThe fun
Page 319 and 320:
fminconx = fmincon(fun,x0,A,b) star
Page 321 and 322:
fminconfunThe function to be minimi
Page 323 and 324: fminconthen the function nonlcon mu
Page 325 and 326: fmincongradhessianlambdaoutputGradi
Page 327 and 328: fminconthe values of these fields i
Page 329 and 330: fminconHessianHessMultIf 'on', fmin
Page 331 and 332: fminconPrecondBandWidth Upper bandw
Page 333 and 334: fminconSince both constraints are l
Page 335 and 336: fmincon• A dense (or fairly dense
Page 337 and 338: fminconReferences[1] Coleman, T.F.
Page 339 and 340: fminimaxx = fminimax(fun,x,A,b,Aeq,
Page 341 and 342: fminimaxfunThe function to be minim
Page 343 and 344: fminimaxIf nonlcon returns a vector
Page 345 and 346: fminimaxlambdamaxfvaloutputStructur
Page 347 and 348: fminimaxMeritFunctionMinAbsMaxOutpu
Page 349 and 350: fminimaxx0 = [0.1; 0.1]; % Make a s
Page 351 and 352: fminimax[3] Han, S.P., “A Globall
Page 353 and 354: fminsearchInputArguments“Function
Page 355 and 356: fminsearchOutputFcnPlotFcnsTolFunSp
Page 357 and 358: fminsearcha = sqrt(2);banana = @(x)
Page 359 and 360: fminuncPurposeEquationFind minimum
Page 361 and 362: fminuncfunThefunctiontobeminimized.
Page 363 and 364: fminuncexitflaggradhessianoutputInt
Page 365 and 366: fminuncLarge-Scale and Medium-Scale
Page 367 and 368: fminuncHessianHessMultIf 'on', fmin
Page 369 and 370: fminuncPrecondBandWidthTolPCGUpper
Page 371 and 372: fminuncx0 = [1,1];[x,fval] = fminun
Page 373: fminunc“Trust-Region Methods for
Page 377 and 378: fseminf“Avoiding Global Variables
Page 379 and 380: fseminfoptions“Options” on page
Page 381 and 382: fseminflambdaoutput5 Magnitude of d
Page 383 and 384: fseminfOutputFcnPlotFcnsRelLineSrch
Page 385 and 386: fseminfSecond, write an M-file, myc
Page 387 and 388: fseminfThe plot command inside 'myc
Page 389 and 390: fseminfThe goal was to minimize the
Page 391 and 392: fsolvePurposeEquationSolve system o
Page 393 and 394: fsolvefunThe nonlinear system of eq
Page 395 and 396: fsolvefuncCountalgorithmcgiteration
Page 397 and 398: fsolvePlotFcnsTolFunPlots various m
Page 399 and 400: fsolveJacobPatternMaxPCGIterPrecond
Page 401 and 402: fsolve[x,fval] = fsolve(@myfun,x0,o
Page 403 and 404: fsolveYoucanformulateandsolvethepro
Page 405 and 406: fsolveLimitationsThe function to be
Page 407 and 408: fzeroPurposeSyntaxDescriptionFind r
Page 409 and 410: fzeroDisplayFunValCheckOutputFcnLev
Page 411 and 412: fzerowrite an M-file called f.m.fun
Page 413 and 414: fzmultPurposeSyntaxMultiplication w
Page 415 and 416: linprogPurposeEquationSolve linear
Page 417 and 418: linproglambdaoutput-2 No feasible p
Page 419 and 420: linprogsubject toFirst, enter the c
Page 421 and 422: linprogDiagnosticsLarge-Scale Optim
Page 423 and 424: linprogthe primal objective < -1e+1
Page 425 and 426:
lsqcurvefitPurposeEquationSolve non
Page 427 and 428:
lsqcurvefitfunThe function you want
Page 429 and 430:
lsqcurvefitoutputupperUpper bounds
Page 431 and 432:
lsqcurvefitJacobianMaxFunEvalsMaxIt
Page 433 and 434:
lsqcurvefitJacobPatternMaxPCGIterSp
Page 435 and 436:
lsqcurvefitNote that at the time th
Page 437 and 438:
lsqcurvefitof J with many nonzeros,
Page 439 and 440:
lsqlinPurposeEquationSolve constrai
Page 441 and 442:
lsqlinlambdaoutput3 Change in the r
Page 443 and 444:
lsqlinDiagnosticsDisplayMaxIterTypi
Page 445 and 446:
lsqlinPrecondBandWidthUpper bandwid
Page 447 and 448:
lsqlinNotesFor problems with no con
Page 449 and 450:
lsqlinReferences[1] Coleman, T.F. a
Page 451 and 452:
lsqnonlinreturn a vector of values
Page 453 and 454:
lsqnonlinOutputArguments“Function
Page 455 and 456:
lsqnonlinalgorithm. See “Optimiza
Page 457 and 458:
lsqnonlinJacobMultFunction handle f
Page 459 and 460:
lsqnonlinfor(that is, F should have
Page 461 and 462:
lsqnonlinand Requirements on page 2
Page 463 and 464:
lsqnonnegPurposeEquationSolve nonne
Page 465 and 466:
lsqnonneglambdaoutputVector contain
Page 467 and 468:
optimgetPurposeSyntaxDescriptionExa
Page 469 and 470:
optimsetIn the following lists, val
Page 471 and 472:
optimsetLineSearchType'cubicpoly' |
Page 473 and 474:
optimtoolPurposeSyntaxDescriptionTo
Page 475 and 476:
quadprogPurposeEquationSolve quadra
Page 477 and 478:
quadproglambdaoutput3 Change in the
Page 479 and 480:
quadprogLargeScaleUse large-scale a
Page 481 and 482:
quadprogTolPCGTermination tolerance
Page 483 and 484:
quadprogNotesIn general quadprog lo
Page 485 and 486:
quadprogWhen the equality constrain
Page 487 and 488:
IndexIndex ε-Constraint method 3-4
Page 489 and 490:
Indexinfeasible solution warninglin
Page 491 and 492:
Indexdescriptions 6-8possible value
show all

What Is Optimization Toolbox?

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?