[工学]第二讲 无约束最优化.ppt

第二讲 无约束非线性规划 fminbnd fminunc fminsearch 函数 2.1 单变量最小化 1、基本数学原理 一维有哪些信誉好的足球投注网站问题,某些情况直接用于求解实际问题,也是进行多变量最优化的基础. minf(x) x1xx2 该问题的有哪些信誉好的足球投注网站过程用下式表达： Xk+1=xk+α*d Xk 为本次迭代的值； α 为有哪些信誉好的足球投注网站方向上的步长参数； d 有哪些信誉好的足球投注网站方向 2、求解方法 拟牛顿法 3、MATLAB求解函数fminbnd 单变量函数求最小值的标准形式为 sub.to 有关参数说明 若参数exitflag0，表示函数收敛于x， 若exitflag=0，表示超过函数估计值或迭代的最大数字， exitflag0表示函数不收敛于x； 若参数output的字段中： iterations 表示迭代次数， funccount 表示函数赋值次数， algorithm 表示所使用的算法， message 退出消息 The function to be minimized. fun takes a scalar x and returns a scalar value f of the objective function evaluated at x. You can specify fun to be an inline object. For example, x = fminbnd(inline(sin(x*x)),x0) Alternatively, fun can be a string containing the name of a function(an M-file, a built-in function, or a MEX-file). If fun=myfun then the M-file function myfun.m would have the form function f = myfun(x) f = ... % Compute function value at x options Optimization parameter options. You can set or change the values of these parameters using the optimset function. fminbnd uses these options structure fields: ?Display – Level of display. off displays no output; iter‘ displays output at each iteration; final displays just the final output. ?MaxFunEvals – Maximum number of function evaluations allowed. ?MaxIter – Maximum number of iterations allowed. ?TolX – Termination tolerance on x. exitflag Describes the exit condition: ? 0 indicates that the function converged to a solution x. ?0 indicates that the maximum number of function evaluations or iterations was reached. ? 0 indicates that the function did not converge to a solution. output A structure whose fields contain information about the optimization: ?output.iterations – The number of iterations taken. ?output.algorithm – The algorithm used. ?output.funcCount – The number of function evaluations Examples A minimum of sin(x) occurs at x = fminbnd(sin,0,2*pi) x = 4.7124 The value of the function