一类半可微优化问题的解集

Solution Sets of a Class of Semidifferentiable Optimization Problems

本文考虑线性约束条件下连续与半可微的伪线性(既伪凸又伪凹)函数的优化问题.使用伪线性函数的性质推导了解集的一般表达式,并基于用右侧导数代替既约梯度的广义凸单纯形法,给出了唯一解的条件以及当唯一性条件不满足时求出解集的计算步骤,最后给出了算例。

The problem of optimizing a continuous and semidifferentiable pseudolinear（both pseudoconvex and pseudoconcave）function with linear constraints is considered.By means of the properties of pseudolinearity,the general expression for the solution set is derived.Based on the extended convex simplex method that uses right-sided derivatives instead of reduced gradient vector,the uniqueness condition of the solution and the computational procedure to find out the solution set（if the uniqueness condition is not satisfied）are provided.Finally,an illustrative example is also given.