What Is Optimization Toolbox?
What Is Optimization Toolbox? What Is Optimization Toolbox?
fminuncY is a matrix that has the same number of rowsas there are dimensions in the problem. W =H*Y although H is not formed explicitly. fminuncuses Hinfo to compute the preconditioner. Theoptional parameters p1, p2, ... can be anyadditional parameters needed by hmfun. See“Avoiding Global Variables via Anonymous andNested Functions” on page 2-20 for informationon how to supply values for the parameters.Note 'Hessian' must be set to 'on' for Hinfoto be passed from fun to hmfun.HessPatternMaxPCGIterSee “Nonlinear Minimization with a Dense butStructured Hessian and Equality Constraints”on page 2-61 for an example.Sparsity pattern of the Hessian for finitedifferencing. If it is not convenient to computethesparseHessianmatrixH in fun, thelarge-scale method in fminunc can approximateH via sparse finite differences (of the gradient)provided the sparsity structure of H —i.e.,locations of the nonzeros—is supplied as thevalue for HessPattern. Intheworstcase,ifthestructure is unknown, you can set HessPatternto be a dense matrix and a full finite-differenceapproximation is computed at each iteration(this is the default). This can be very expensivefor large problems, so it is usually worth theeffort to determine the sparsity structure.Maximum number of PCG (preconditionedconjugate gradient) iterations (see “Algorithms”on page 8-88).8-84
fminuncPrecondBandWidthTolPCGUpper bandwidth of preconditioner for PCG. Bydefault, diagonal preconditioning is used (upperbandwidth of 0). For some problems, increasingthe bandwidth reduces the number of PCGiterations. Setting PrecondBandWidth to 'Inf'uses a direct factorization (Cholesky) ratherthan the conjugate gradients (CG). The directfactorization is computationally more expensivethan CG, but produces a better quality steptowards the solution.Termination tolerance on the PCG iteration.Medium-Scale Algorithm OnlyThese options are used only by the medium-scale algorithm:8-85
- 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: fminuncHessianHessMultIf 'on', fmin
- Page 371 and 372: fminuncx0 = [1,1];[x,fval] = fminun
- Page 373 and 374: fminunc“Trust-Region Methods for
- Page 375 and 376: fseminfPurposeEquationFind minimum
- 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
fminuncY is a matrix that has the same number of rowsas there are dimensions in the problem. W =H*Y although H is not formed explicitly. fminuncuses Hinfo to compute the preconditioner. Theoptional parameters p1, p2, ... can be anyadditional parameters needed by hmfun. See“Avoiding Global Variables via Anonymous andNested Functions” on page 2-20 for informationon how to supply values for the parameters.Note 'Hessian' must be set to 'on' for Hinfoto be passed from fun to hmfun.HessPatternMaxPCGIterSee “Nonlinear Minimization with a Dense butStructured Hessian and Equality Constraints”on page 2-61 for an example.Sparsity pattern of the Hessian for finitedifferencing. If it is not convenient to computethesparseHessianmatrixH in fun, thelarge-scale method in fminunc can approximateH via sparse finite differences (of the gradient)provided the sparsity structure of H —i.e.,locations of the nonzeros—is supplied as thevalue for HessPattern. Intheworstcase,ifthestructure is unknown, you can set HessPatternto be a dense matrix and a full finite-differenceapproximation is computed at each iteration(this is the default). This can be very expensivefor large problems, so it is usually worth theeffort to determine the sparsity structure.Maximum number of PCG (preconditionedconjugate gradient) iterations (see “Algorithms”on page 8-88).8-84