Exactness of penalization for exact minimax penalty function method in nonconvex programming  

作　　者：T.ANTCZAK 

机构地区：[1]Faculty of Mathematics and Computer Science,University of Lódz

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第4期541-556,共16页应用数学和力学（英文版）

摘　　要：The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.The exact minimax penalty function method is used to solve a noncon- vex differentiable optimization problem with both inequality and equality constraints. The conditions for exactness of the penalization for the exact minimax penalty function method are established by assuming that the functions constituting the considered con- strained optimization problem are invex with respect to the same function η （with the exception of those equality constraints for which the associated Lagrange multipliers are negative these functions should be assumed to be incave with respect to η）. Thus, a threshold of the penalty parameter is given such that, for all penalty parameters exceeding this threshold, equivalence holds between the set of optimal solutions in the considered constrained optimization problem and the set of minimizer in its associated penalized problem with an exact minimax penalty function. It is shown that coercivity is not suf- ficient to prove the results.

关 键 词：exact minimax penalty function method minimax penalized optimizationproblem exactness of penalization of exact minimax penalty function invex function incave function 

分 类 号：O224[理学—运筹学与控制论]