一类半定二次规划逆问题  

Solving a Class of Inverse Semidefinite Quadratic Programming Problem

作　　者：李丽丹[1] 郭燕 徒君[1] LI LIDAN;GUO YAN;TU JUN(College of Science,Liaoning Technical University,Fuxin 123000,China)

机构地区：[1]辽宁工程技术大学理学院,阜新123000

出　　处：《应用数学学报》2022年第4期533-551,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(51704140);辽宁省教育厅科学研究经费项目(LJ2020QNL008);辽宁省自然科学基金(2021-MS-340);辽宁省教育厅基金(LJKZ0347)资助项目.

摘　　要：本文求解了一类半定二次规划的逆问题、具体可描述为在保证一个可行的解是原半定二次规划问题的最优解的前提下,使目标函数中的参数以及约束条件中右端项参数与它们的估计值的距离最小我们将该逆问题转换为具有线性约束和半正定锥互补约束的问题.再利用对偶理论,又将上述问题转化成只有半正定锥互补约束的问题,但此时也是一个难问题,通过引入一个非光滑的惩罚函数来惩罚互补约束,进而将原问题转化为一个DC问题、再采用序列凸规划方法来求解它,同时给出惩罚方法以及序列凸规划方法的收敛性分析.最后的数值实验表明我们采用的方法对于本文提出的问题求解还是非常有效的.In this paper,a class of inverse Semidefinite quadratic programming(SDQP)problem is solved.It can be described as that the parameters in both the objective function and the constraint set of a given SDQP problem need to be adjusted as little as possible so that a known feasible solution becomes the optimal one.We formulate the inverse problem into a problem with linear constraint and semidefinite cone complementaxy constraint.By using the duality theory,the above problem is transformed into a problem with only semidefinite cone complementary constraints which is a rather difficult problem.By introducing a non smooth penalty function to penalize the complementary constraint,the inverse problem is transformed into a DC programming problem.We use sequential convex programming method to solve it and give the convergence analysis of sequential convex programming method and penalty method.Finally,numerical experiments show that out method is very effective for solving the inverse problem proposed in this paper.

关 键 词：逆问题 半定二次规划问题 序列凸规划 惩罚方法 

分 类 号：O221.2[理学—运筹学与控制论]