fmincon.rar_fmincon_fmincon_fminconfunction_fmincon函数_matlab

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fmincon优化函数.doc 85KB

您所在位置：编程爱好者网站 — 编程爱好者论坛 — 请教一下 fmincon 函数的使用？

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主题：请教一下 fmincon 函数的使用？

作者：headtohead 发表时间：2008-6-7 23:17:00

楼主

求最小值，不知道 fmincon 里面 A,b,Aeq,Beq,Lb,Ub,nonlcon,options 分别怎么写，谢谢

作者：ronei 发表时间：2008-6-8 6:25:00

　第 1 楼

查查 help 文件不就都有了嘛

FMINCON finds a constrained minimum of a function of several variables.

FMINCON attempts to solve problems of the form:

min F(X) subject to: A*X <= B, Aeq*X = Beq (linear constraints)

X C(X) <= 0, Ceq(X) = 0 (nonl

inear constraints)

LB <= X <= UB

(bounds)

X=FMINCON(FUN,X0,A,B) starts at X0 and finds a minimum X to the function

FUN, subject to the linear inequalities A*X <= B. FUN accepts input X and

returns a scalar function value F evaluated at X. X0 may be a scalar,

vector, or matrix.

X=FMINCON(FUN,X0,A,B,Aeq,Beq) minimizes FUN subject to the linear equalities

Aeq*X = Beq as well as A*X <= B. (Set A=[] and B=[] if no inequalities exist

X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB) defines a set of lower and upper

bounds on the design variables, X, so that a solution is found in

the range LB <= X <= UB. Use empty matrices for LB and UB

if no bounds exist. Set LB(i) = -Inf if X(i) is unbounded below;

set UB(i) = Inf if X(i) is unbounded above.

X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON) subjects the minimization to the

constraints defined in NONLCON. The function NONLCON accepts X and returns

the vectors C and Ceq, representing the nonlinear inequalities and equalities

respectively. FMINCON minimizes FUN such that C(X)<=0 and Ceq(X)=0.

(Set LB=[] and/or UB=[] if no bounds exist.)

作者：ronei 发表时间：2008-6-8 6:25:00

　第 2 楼

X=FMINCON(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS) minimizes with the

default optimization parameters replaced by values in the structure

OPTIONS, an argument created with the OPTIMSET function. See OPTIMSET

for details. Used options are Display, TolX, TolFun, TolCon,

DerivativeCheck, Diagnostics, FunValCheck, GradObj, GradConstr,

Hessian, MaxFunEvals, MaxIter, DiffMinChange and DiffMaxChange,

LargeScale, MaxPCGIter, PrecondBandWidth, TolPCG, TypicalX, Hessian,

HessMult, HessPattern, PlotFcns, and OutputFcn. Use the GradObj option

to specify that FUN also returns a second output argument G that is the

partial derivatives of the function df/dX, at the point X. Use the Hessian

option to specify that FUN also returns a third output argument H that

is the 2nd partial derivatives of the function (the Hessian) at the

point X. The Hessian is only used by the large-scale method, not the

line-search method. Use the GradConstr option to specify that NONLCON

also returns third and fourth output arguments GC and GCeq, where GC is

the partial derivatives of the constraint vector of inequalities C, and

GCeq is the partial derivatives of the constraint vector of equalities

Ceq. Use OPTIONS = [] as a place holder if no options are set.

X=FMINCON(PROBLEM) finds the minimum for PROBLEM. PROBLEM is a

structure with the function FUN in PROBLEM.objective, the start point

in PROBLEM.x0, the linear inequality constraints in PROBLEM.Aineq

and PROBLEM.bineq, the linear equality constraints in PROBLEM.Aeq and

PROBLEM.beq, the lower bounds in PROBLEM.lb, the upper bounds in

PROBLEM.ub, the nonlinear constraint function in PROBLEM.nonlcon, the

options structure in PROBLEM.options, and solver name 'fmincon' in

PROBLEM.solver. Use this syntax to solve at the command line a problem

exported from OPTIMTOOL. The structure PROBLEM must have all the fields.

[X,FVAL]=FMINCON(FUN,X0,...) returns the value of the objective

function FUN at the solution X.

[X,FVAL,EXITFLAG]=FMINCON(FUN,X0,...) returns an EXITFLAG that describes the

exit condition of FMINCON. Possible values of EXITFLAG and the corresponding

exit conditions are listed below.

Both medium- and large-scale:

1 First order optimality conditions satisfied to the specified tolerance.

0 Maximum number of function evaluations or iterations reached.

-1 Optimization terminated by the output function.

Large-scale only:

2 Change in X less than the specified tolerance.

3 Change in the objective function value less than the specified tolerance.

Medium-scale only:

4 Magnitude of search direction smaller than the specified tolerance and

constraint violation less than options.TolCon.

5 Magnitude of directional derivative less than the specified tolerance

and constraint violation less than options.TolCon.

-2 No feasible point found.

作者：ronei 发表时间：2008-6-8 6:26:00

　第 3 楼

[X,FVAL,EXITFLAG,OUTPUT]=FMINCON(FUN,X0,...) returns a structure OUTPUT with

the number of iterations taken in OUTPUT.iterations, the number of function

evaluations in OUTPUT.funcCount, the norm of the final step in OUTPUT.stepsize,

the algorithm used in OUTPUT.algorithm, the first-order optimality in

OUTPUT.firstorderopt, and the exit message in OUTPUT.message. The medium scale

algorithm returns the final line search steplength in OUTPUT.lssteplength, and

the large scale algorithm returns the number of CG iterations in OUTPUT.cgiterati

ons.

[X,FVAL,EXITFLAG,OUTPUT,LAMBDA]=FMINCON(FUN,X0,...) returns the Lagrange multipliers

at the solution X: LAMBDA.lower for LB, LAMBDA.upper for UB, LAMBDA.ineqlin is

for the linear inequalities, LAMBDA.eqlin is for the linear equalities,

LAMBDA.ineqnonlin is for the nonlinear inequalities, and LAMBDA.eqnonlin

is for the nonlinear equalities.

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