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This paper presents a new penalty function called logarithmic penalty function (LPF) and examines the convergence of the proposed LPF method. Furthermore, the LaGrange multiplier for equality constrained optimization is derived based on the first-order necessary condition. | Nội dung Text A new logarithmic penalty function approach for nonlinear constrained optimization problem Decision Science Letters 8 2019 353 362 Contents lists available at GrowingScience Decision Science Letters homepage www.GrowingScience.com dsl A new logarithmic penalty function approach for nonlinear constrained optimization problem Mansur Hassana b and Adam Baharuma aSchool of Mathematical Sciences Universiti Sains Malaysia 11800 USM Penang Malaysia bDepartment of Mathematics Yusuf Maitama Sule University Kano 700241 Kabuga Kano Nigeria CHRONICLE ABSTRACT Article history This paper presents a new penalty function called logarithmic penalty function LPF and Received July 9 2018 examines the convergence of the proposed LPF method. Furthermore the LaGrange multiplier Received in revised format for equality constrained optimization is derived based on the first-order necessary condition. The August 10 2018 proposed LPF belongs to both categories a classical penalty function and an exact penalty Accepted August 30 2018 Available online function depending on the choice of penalty parameter. Moreover the proposed LPF is capable August 31 2018 of dealing with some of the problems with irregular features from Hock-Schittkowski collections Keywords of test problems. Nonlinear optimization Logarithmic penalty function Penalized optimization problem 2018 by the authors licensee Growing Science Canada. 1. Introduction In this paper we consider the following nonlinear constrained optimization problem P 0 1 2 where and are continuously differentiable functions on a nonempty set . For the sake of simplicity let 0 1 2 be the set of all feasible solutions for the constrained optimization problem P . The problem P has many practical applications in engineering decision theory economics etc. The area has received much concern and it is growing significantly in different directions. Many researchers are working tirelessly to explore various methods that might be advantageous in
