卡鲁什-库恩-塔克条件
数学
数学优化
线性化
拉格朗日乘数
最优化问题
序列(生物学)
极限(数学)
趋同(经济学)
功能(生物学)
应用数学
非线性系统
数学分析
生物
物理
进化生物学
量子力学
遗传学
经济
经济增长
作者
Alexander S. Strekalovsky,Ilya Minarchenko
标识
DOI:10.1016/j.apm.2017.07.031
摘要
This paper addresses a nonconvex optimization problem with the cost function and inequality constraints given by d.c. functions. The original problem is reduced to a problem without inequality constraints by the exact penalization procedure. A special local search method for the penalized problem is developed, which is based, first, on the linearization procedure with respect to the basic nonconvexity and, second, on the consecutive solutions of linearized convex problems. Convergence properties of the method are investigated. In particular, it is shown that a limit point of the sequence produced by the method is considerably stronger than the usual KKT-vector. In addition, the relations between an approximate solution of linearized convex problem and the KKT-vector of the original problem are established, and the various stopping criteria are substantiated. Besides, we established the relations among the Lagrange multipliers of the original problem, those ones of the linearized problem, and the value of the penalty parameter. Finally, a preliminary computational testing of the LSM developed has been carried out on several test problems taken from literature.
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