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

Abstract

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

A review of methods and algorithms for optimizing construction scheduling

“…The method integrates the constraints into the objective function by using several penalty parameters such that the original constrained optimization problem is transformed into an unconstrained optimization problem. It is shown that if the value of the penalty parameter is sufficiently large, then any local minimizer of the corresponding unconstrained optimization problem is a local minimizer of the original problem (Yu et al, 2010). With such a transformation, many existing methods can be utilized to deal with the unconstrained optimization problem, which makes the problem much easier to solve.…”

“…It is suggested that future research in construction scheduling should consider the application of the exact penalty function method for constrained optimization problems (Yu et al, 2010). The method integrates the constraints into the objective function by using several penalty parameters such that the original constrained optimization problem is transformed into an unconstrained optimization problem.…”

“…Thus, the original single objective optimization problem (ie, optimal time or cost) is shifted to a bi-objective optimization problem (ie, optimal time-cost). The construction time-cost optimization problem has been examined extensively in the construction engineering and management literature (eg, Siemens, 1971;Tamimi and Diekmann, 1988;Que, 2002;Rogalska et al, 2008;Wu et al, 2009;Yu et al, 2010;Wongwai and Malaikrisanachalee, 2011).…”

An evolutionary hybrid method to predict pistachio price

“…PSO, as a type of simple and effective random searching algorithm, may lead to better results than the gradient descent method, penalty function method, and genetic algorithm, when solving some non-linear optimization problems [34,35].…”

An interior penalty method for optimal control problems with state and input constraints of nonlinear systems

“…There exist also recent works in the field of exact penalty methods for various types of optimal control problem [24][25][26][27][28][29]. These methods are of particular interest because each solution of the sequence of optimal control problem is easily computed using classical stationarity conditions of the solution.…”