What Is Optimization Toolbox?

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AcknowledgmentsAcknowledgmentsTheMathWorkswouldliketoacknowledgethefollowingcontributorstoOptimization Toolbox.Thomas F. Coleman researched and contributed the large-scale algorithmsfor constrained and unconstrained minimization, nonlinear least squares andcurve fitting, constrained linear least squares, quadratic programming, andnonlinear equations.Dr. Coleman is Dean of Faculty of Mathematics and Professor ofCombinatorics and Optimization at University of Waterloo.Dr. Coleman has published 4 books and over 70 technical papers in theareas of continuous optimization and computational methods and tools forlarge-scale problems.Yin Zhang researched and contributed the large-scale linear programmingalgorithm.Dr. Zhang is Professor of Computational and Applied Mathematics on thefaculty of the Keck Center for Interdisciplinary Bioscience Training at RiceUniversity.Dr. Zhang has published over 50 technical papers in the areas of interior-pointmethods for linear programming and computation mathematicalprogramming.
Page 1 and 2: Optimization Toolbox 3User’s Guid
Page 3: Revision HistoryNovember 1990 First
Page 7 and 8: Contents1Getting StartedWhat Is Opt
Page 9 and 10: Other Examples That Use this Techni
Page 11 and 12: Main Algorithm ....................
Page 13 and 14: 7Functions — By CategoryMinimizat
Page 15 and 16: 1Getting StartedWhat Is Optimizatio
Page 17 and 18: What Is Optimization Toolbox?proble
Page 19 and 20: Optimization Examplewhereis the nor
Page 21 and 22: 2TutorialThe Tutorial provides info
Page 23 and 24: IntroductionIntroductionOptimizatio
Page 25 and 26: IntroductionEquation SolvingType No
Page 27 and 28: Introductionresulting point where t
Page 29 and 30: Examples That Use Standard Algorith
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Examples That Use Standard Algorith
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Large-Scale ExamplesGenerally speak
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Large-Scale ExamplesLarge-Scale Pro
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Large-Scale ExamplesNonlinear Equat
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Large-Scale Examples'LargeScale','o
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Large-Scale Examples3 16 0.0458181
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Large-Scale ExamplesF = 2 + 2*k-exp
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2 Tutoriali=1:(n-1); g = zeros(n,1)
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2 TutorialThe sparsity pattern of t
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2 Tutorialexitflag =3fval =270.4790
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2 Tutorial2.9310e+006Step 2: Call a
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2 Tutorialto 'on', fmincon knows to
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2 TutorialNorm of First-orderIterat
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2 Tutoriallight of this cost, one s
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2 Tutorial• Contains a nested fun
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2 Tutorialexitflag =3output =iterat
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2 Tutorial[fval,exitflag,output] =
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2 Tutorialload sc50bThis problem in
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2 TutorialBecause the iterative dis
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2 TutorialDefault Options Settings
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2 TutorialSetting More Than One Opt
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2 TutorialFunction-Specific Output
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2 Tutorialfzero and fminbndThe foll
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2 Tutorialfgoalattain,fmincon,fmini
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2 TutorialCalling an Output Functio
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2 TutorialThe arguments that the op
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2 TutorialRunning the ExampleTo run
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2 TutorialThe example displays a pl
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2 Tutorialx = fminbnd(fh, 3, 4)You
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2 TutorialTypicalProblemsandHowtoDe
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2 TutorialTroubleshooting (Continue
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2 TutorialSelected Bibliography[1]H
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3 Standard AlgorithmsLeast-Squares
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3 Standard AlgorithmsOptimization O
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3 Standard AlgorithmsUnconstrained
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3 Standard Algorithms(3-4)The optim
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3 Standard AlgorithmsThe line searc
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3 Standard AlgorithmsThe functions
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3 Standard AlgorithmsCase 3.Case 4.
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3 Standard Algorithmsprocedure, the
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3 Standard AlgorithmsLeast-Squares
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3 Standard AlgorithmsGauss-Newton M
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3 Standard AlgorithmsNonlinear Leas
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3 Standard AlgorithmsThe implementa
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3 Standard Algorithmswhereis the n-
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3 Standard AlgorithmsThe step is co
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3 Standard Algorithmsbe canceled, L
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3 Standard AlgorithmsConsider Rosen
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3 Standard AlgorithmsThe functions
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3 Standard Algorithmsis called the
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3 Standard AlgorithmsLine Search an
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3 Standard AlgorithmsPhase 1. In ph
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3 Standard AlgorithmsWhen the probl
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3 Standard Algorithmsto characteriz
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3 Standard AlgorithmsWeighted Sum M
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3 Standard AlgorithmsFigure 3-11:Ge
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3 Standard AlgorithmsFigure 3-12:Ge
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3 Standard AlgorithmsTo overcome th
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3 Standard Algorithms[12] Fleming,
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3 Standard Algorithms[36] Powell, M
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4 Large-Scale AlgorithmsLarge-Scale
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4 Large-Scale AlgorithmsEquation 4-
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4 Large-Scale AlgorithmsDemos of La
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4 Large-Scale AlgorithmsIn a minimi
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4 Large-Scale AlgorithmsBox Constra
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4 Large-Scale AlgorithmsNonlinear L
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4 Large-Scale AlgorithmsLinear Leas
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4 Large-Scale Algorithms(4-16)which
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4 Large-Scale AlgorithmsThe algorit
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4 Large-Scale AlgorithmsSelected Bi
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4 Large-Scale Algorithms4-22
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5 Optimization ToolGetting Started
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5 Optimization ToolSteps for Using
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5 Optimization ToolSolverfminuncfse
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5 Optimization ToolProblem Setup (C
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5 Optimization Toolfgoalattain Prob
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5 Optimization ToolX2 (required) is
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5 Optimization Toolfminimax Problem
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5 Optimization Toolfminunc Problem
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5 Optimization ToolK1, K2, ..., Knt
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5 Optimization ToolX1 and X2 for wh
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5 Optimization Toollsqcurvefit Prob
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5 Optimization ToolConstraintsLinea
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5 Optimization ToolStart PointStart
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5 Optimization ToolRunning a Proble
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5 Optimization ToolSpecifying the O
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5 Optimization ToolFunction Value C
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5 Optimization ToolFor the medium-s
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5 Optimization ToolThe graphic abov
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5 Optimization Tool• Maximum iter
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5 Optimization ToolThegraphicaboves
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5 Optimization ToolGetting Help in
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5 Optimization ToolThe default valu
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5 Optimization ToolAlthough you can
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5 Optimization Tool-9*x(1)^2 - x(2)
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5 Optimization Tool• The Current
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5 Optimization Toolsubject to the c
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5 Optimization Tool• The Current
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6 Argument and Options ReferenceFun
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6 Argument and Options ReferenceInp
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6 Argument and Options ReferenceOut
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6 Argument and Options ReferenceOpt
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6 Argument and Options ReferenceCor
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6 Argument and Options Referenceopt
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6 Argument and Options Referenceopt
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6 Argument and Options ReferenceSta
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6 Argument and Options Reference6-2
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7 Functions — By CategoryMinimiza
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7 Functions — By Category7-4
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intprogPurposeEquationSolve binary
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intprogexitflagoutputInteger identi
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intprogNodeSearchStrategyStrategy t
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intprog• If the algorithm finds a
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intprogSee Alsolinprog, optimset, o
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fgoalattainPurposeEquationSolve mul
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fgoalattain“Avoiding Global Varia
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fgoalattainnonlconThe function that
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fgoalattainweightA weighting vector
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fgoalattainoutputupper Upper bounds
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fgoalattainPlotFcnsRelLineSrchBndRe
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fgoalattainC = [1 0 0; 0 0 1];K0 =
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fgoalattainmethods assume the funct
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fminbndPurposeEquationFind minimum
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fminbndoutput-1 Algorithm was termi
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fminbndThevalueattheminimumisy = f(
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fminconPurposeEquationFind minimum
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fmincon[x,fval,exitflag,output,lamb
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fminconIftheHessianmatrixcanalsobec
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fminconOutputArguments“Function A
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fminconstepsizefirstorderoptFinal s
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fminconGradObjMaxFunEvalsMaxIterOut
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fminconY is a matrix that has the s
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fminconMedium-Scale Algorithm OnlyT
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fmincon• Specify the feasible reg
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fminconsubproblem at each iteration
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fminimaxPurposeEquationSolve minima
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fminimaxInputArguments“Function A
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fminimaxnonlconThe gradient consist
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fminimaxexitflagInteger identifying
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fminimaxDiffMaxChangeDiffMinChangeD
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fminimaxRelLineSrchBndDurationTolCo
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fminimaxset to 'iter'). The depende
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fminsearchPurposeEquationFind minim
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fminsearchoutput0 Number of iterati
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fminsearch8.1777e-010This indicates
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fminsearchNotesfminsearch is not th
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fminunc[x,fval,exitflag,output,grad
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fminuncThe gradient is the partial
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fminunccgiterationsstepsizeNumber o
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fminuncPlotFcnsTolFunPlots various
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fminuncY is a matrix that has the s
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fminuncHessUpdateMethod for choosin
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fminuncx =1.0e-015 *0.1110 -0.8882f
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fminunc[3] Coleman, T.F. and Y. Li,
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fseminfDescriptionfseminf finds a m
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fseminffunThefunctiontobeminimized.
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fseminfThe vectors or matrices K1,
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fseminfOptionsOptimization options
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fseminfvalues other than the recomm
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fseminf0.4023The function value and
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fseminfs = [2 2];end% Sampling setw
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fseminfAlgorithmLimitationsSee Also
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fsolveInputArguments“Function Arg
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fsolveOutputArguments“Function Ar
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fsolveMedium-Scale and Large-Scale
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fsolveJacobMultFunction handle for
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fsolveNonlEqnAlgorithmSpecify one o
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fsolvestarting at the point x= [1,1
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fsolvedogleg method described in [8
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fsolve[6] Moré, J. J., “The Leve
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fzeroNote For the purposes of this
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fzerooutput-4 Complex function valu
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fzeroAlgorithmLimitationsReferences
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gangstrPurposeSyntaxDescriptionSee
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linprogx = linprog(f,A,b,Aeq,beq,lb
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linprogLargeScaleUse large-scale al
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linprogNonzero elements of the vect
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linprogNote The preprocessing steps
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linprogReferences[1] Dantzig, G.B.,
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lsqcurvefitx = lsqcurvefit(fun,x0,x
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lsqcurvefitOutputArguments“Functi
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lsqcurvefitmedium-scale algorithm.
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lsqcurvefitJacobMultFunction handle
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lsqcurvefitLevenbergMarquardt Choos
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lsqcurvefitcubic polynomial method
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lsqcurvefitSee Also@ (function_hand
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lsqlinx = lsqlin(C,d,A,b,Aeq,beq,lb
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lsqlincgiterationsfirstorderoptNumb
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lsqlinJacobMultFunction handle for
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lsqlin0.6721];lb = -0.1*ones(4,1);u
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lsqlinDiagnosticsLarge-Scale Optimi
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lsqnonlinPurposeEquationSolve nonli
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lsqnonlinfunThe function whose sum
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lsqnonlinoutputupperUpper bounds ub
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lsqnonlinJacobianMaxFunEvalsMaxIter
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lsqnonlinMaxPCGIterMaximum number o
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lsqnonlinGauss-Newton method, which
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lsqnonlin[5] Marquardt, D., “An A
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lsqnonneg[x,resnorm,residual,exitfl
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lsqnonnegAlgorithmNoteslsqnonneg us
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optimsetPurposeSyntaxDescriptionOpt
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optimsetTolFunTolXTypicalXPositive
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optimsetThis statement makes a copy
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optimtoolSee Alsooptimset8-190
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quadprog[x,fval] = quadprog(...) re
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quadprogalgorithmcgiterationsfirsto
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quadprogHessMultFunction handle for
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quadprogNext, invoke a quadratic pr
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quadprogAlgorithmLarge-Scale Optimi
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quadprog[2] Gill, P. E. and W. Murr
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Indexlarge-scale 4-9equation solvin
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Indexmerit function 3-38minimax exa
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Indexdetermination of 4-4subspace,
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