CAJ | 학술논문

寻找数学规划问题的多个最优解乃至最优解集是一项有理论价值和实践意义的工作，因为决策者可以从多个最优解中挑选其满意的最佳方案。然而，目前有关寻求非线性规划问题多个最优解的研究还比较少见且存在局限性。研究了伪凸目标函数的二次规划问题，首先提出和证明了最优解集的特征，然后借助于求解带有人工变量的辅助线性规划全部最优解的方法，提出了伪凸二次规划有唯一最优解的条件，并在不满足该条件的情况下，通过寻找辅助线性规划的最优解集以获得伪凸二次规划的最优解集。最后给出了两个算例以说明方法的有效性。
심조수학규화문제적다개최우해내지최우해집시일항유이론개치화실천의의적공작，인위결책자가이종다개최우해중도선기만의적최가방안。연이，목전유관심구비선성규화문제다개최우해적연구환비교소견차존재국한성。연구료위철목표함수적이차규화문제，수선제출화증명료최우해집적특정，연후차조우구해대유인공변량적보조선성규화전부최우해적방법，제출료위철이차규화유유일최우해적조건，병재불만족해조건적정황하，통과심조보조선성규화적최우해집이획득위철이차규화적최우해집。최후급출료량개산례이설명방법적유효성。
To find multiple optimal solutions and even the optimal solution set to the mathematical program-ming problem is a significant work both in theory and practice because the specific optimal plan that is most de-sirable can be selected by the decision maker.However,the study on finding multiple optimal solutions to the nonlinear programming problem for now is seldom seen and has limitations.The quadratic programming prob-lem with the pseudoconvex objective function is considered.Firstly,the characteristic of the optimal solution set is presented and proved.Then,by the approach of finding all optimal solutions to an auxiliary linear pro-gramming with artificial variables,a condition for the unique optimal solution to the pseudoconvex quadratic programming is presented,and in the case that the condition is not sattisfied,the optimal solution set to the pseudoconvex quadratic programming is obtained by means of finding the optimal solution set to the auxiliary linear programming.Finally,two computational examples are also given to illustrate the effectiveness of the method.