Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques, which is based on Mathematical Programming with Equilibrium Constraints (MPECs). We first reformulate the binary program as an equivalent augmented biconvex optimization problem with a bilinear equality cons...

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 ...

We propose an exact penalty approach for solving mixed integer nonlinear programming (MINLP) problems by converting a general MINLP problem to a finite sequence of nonlinear programming (NLP) problems with only continuous variables. We express conditions of exactness for MINLP problems and show how the exact penalty approach can be extended to constrained problems.

A new and universal penalty method is introduced in this contribution. It is especially intended to be applied in stochastic metaheuristics like genetic algorithms, particle swarm optimization or ant colony optimization. The novelty of this method is, that it is an advanced approach that only requires one parameter to be tuned. Moreover this parameter, named oracle, is easy and intuitive to han...

Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of...

In this paper we introduced and analyzed the Log-Sigmoid (LS) multipliers method for constrained optimization. The LS method is to the recently developed smoothing technique as augmented Lagrangian to the penalty method or modified barrier to classical barrier methods. At the same time the LS method has some specific properties, which make it substantially different from other nonquadratic augm...

In this article, element free Galerkin method is used for static analysis of thin micro/nanoscale plates based on the nonlocal plate theory. The problem is solved for the plates with arbitrary boundary conditions. Since shape functions of the element free Galerkin method do not satisfy the Kronecker’s delta property, the penalty method is used to impose the essential boundary conditions. Discre...