On the penalization method in mathematical programming
Well known in mathematical programming (MP) are the techniques of equivalent and asymptotic reduction of constrained optimization problems to unconstrained ones, more precisely, to problems in which any part of the original constraints is accumulated by a modified objective function. These techniques are of fundamental importance: they not only generate new methods for solving optimization problems but are the basis for many theoretical principles of MP, for example, optimality conditions, modified Lagrange functions, duality for improper problems in MP, and other. Such techniques continue to attract interest. We first state some equivalence theorems, give estimates of the constraint residuals and then apply the penalization method to (1) the problem of sequential correction of an improver linear programming problem of the first kind, (2) the problem of sequential Pareto correction of an improper problem of piecewise linear programming. Finally we discuss the nondifferentiability of the penalty function as a necessary condition for equivalent reduction. All results are stated without proofs.
sequential correction of an improver linear programming
scientific article; zbMATH DE number 1099477