第四章非线性规划.doc

第四章 非线性规划 本章, 我们介绍两种解决非线性规划问题的软件: 第一种: MATLAB中的optimization toolbox 中的若干程序; 第二种: LINGO软件. 1．MATLAB程序说明 1.1 无约束问题 程序名: unpfun1函数, unpfun2函数 unpfun1 实例: Minimize the function 在命令窗口输入以下信息: x0=[1,1]; % Then call fminunc to find a minimum of unpfun1 near [1,1] [x,fval]=fminunc(@unpfun1,x0) 输出以下信息: Optimization terminated successfully: Search direction less than 2*options.TolX x = 1.0e-008 * -0.7591 0.2665 fval = 1.3953e-016 unpfun2实例：将上述的实例用梯度法做 在命令窗口输入以下信息: options = optimset(GradObj,on); % To minimize this function with the gradient provided x0 = [1,1]; [x,fval] = fminunc(@unpfun2,x0,options) 输出以下信息: Optimization terminated successfully: First-order optimality less than OPTIONS.TolFun, and no negative/zero curvature detected x = 1.0e-015 * 0.1110 -0.8882 fval = 6.2862e-031 程序的相关知识： 第一种: fminsearch Find a minimum of an unconstrained multivariable function where x is a vector and f(x) is a function that returns a scalar. 语法如下: x = fminsearch(fun,x0) x = fminsearch(fun,x0,options) [x,fval] = fminsearch(...) [x,fval,exitflag] = fminsearch(...) [x,fval,exitflag,output] = fminsearch(...) 解释: fminsearch attempts to find a minimum of a scalar function of several variables, starting at an initial estimate. This is generally referred to as unconstrained nonlinear optimization. x = fminsearch(fun,x0) starts at the point x0 and attempts to find a local minimum x of the function described in fun. fun is a function handle for either an M-file function or an anonymous function. x0 can be a scalar, vector, or matrix. x = fminsearch(fun,x0,options) minimizes with the optimization options specified in the structure options. Use optimset to set these options. [x,fval] = fminsearch(...) returns in fval the value of the objective function fun at the solution x. [x,fval,exitflag] = fminsearch(...) returns a value exitflag that describes the exit condition of fminsearch. [x,fval,exitflag,output] = fminsearch(...) returns a structure output that contains informatio