On the exactness and the convergence of the $$l_{1}$$ exact penalty E-function method for E-differentiable optimization problems

Abstract

AbstractThis paper is devoted to introduce and investigate a new exact penalty function method which is called the $$l_{1}$$ l 1 exact penalty E-function method. Namely, we use the aforesaid exact penalty function method to solve a completely new class of nonconvex (not necessarily) differentiable mathematical programming problems, that is, E-differentiable minimization problems. Then, we analyze the most important from a practical point of view property of all exact penalty function methods, that is, exactness of the penalization. Thus, under appropriate E-convexity hypotheses, we prove the equivalence between the original E-differentiable extremum problem and its corresponding penalized optimization problem created in the introduced $$l_{1}$$ l 1 exact penalty E-function method. Further, we also present and investigate the algorithm for this exact penalty function method which minimizes the $$l_{1}$$ l 1 exact penalty E-function. The convergence theorem for the aforesaid algorithm is also established.