A new exact penalty function method for continuous inequality constrained optimization problems

In this paper, a computational approach based on a new exact penaltyfunction method is devised for solving a class of continuousinequality constrained optimization problems. The continuousinequality constraints are first approximated by smooth function inintegral form. Then, we construct a new exact penalty function,where the summation of all these approximate smooth functions inintegral form, called the constraint violation, is appended to theobjective function. In this way, we obtain a sequence of approximateunconstrained optimization problems. It is shown that if the valueof the penalty parameter is sufficiently large, then any localminimizer of the corresponding unconstrained optimization problem isa local minimizer of the original problem. For illustration, threeexamples are solved using the proposed method. From the solutionsobtained, we observe that the values of their objective functionsare amongst the smallest when compared with those obtained by otherexisting methods available in the literature. More importantly, ourmethod finds solution which satisfies the continuous inequalityconstraints.