The Gerber-Shiu function provides a unified framework for the evaluation of variety risk quantities. Ever since its establishment, it has attracted constantly increasing interests in actuarial science, whereas conventional research been focused on finding analytical or semi-analytical solutions, either which is rarely available, except limited classes penalty functions rather simple models. In ...

A new projective exact penalty function method is proposed for the equivalent reduction of constrained optimization problems to unconstrained ones. In method, original objective extended infeasible points by summing its value at projection an point on feasible set with distance set. The equivalence means that local and global minimums coincide. Nonconvex sets multivalued projections are admitte...

This paper addresses the Tardy/Lost penalty minimization on a single machine. According to this penalty criterion, if the tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. Besides its application in real world problems, Tardy/Lost measure is a general form for popular objective functions like weighted tardiness, late work and tardiness with reje...

Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using genetic algorithms (GAs) or classical optimization methods, penalty function methods have been the most popular approach, because of their simplicity and ease of implementation. However...