We present a general theory of exact penalty functions with vectorial (multidimensional) parameter for optimization problems in infinite dimensional spaces. In comparison the scalar case, use parameters provides much more flexibility, allows one to adaptively and independently take into account violation each constraint during an process, often leads better overall performance method using func...

We propose a new class of Foundation-Penalty (FP) cuts for GUB-constrained (and ordinary) mixed-integer programs, which are easy to generate by exploiting standard penalty calculations that are routinely employed in branch-and-bound contexts. The FP cuts are derived with reference to a selected integer variable or GUB set, and a foundation function that is typically a reduced cost function corr...

Optimum laminate configuration for minimum weight of filament–wound laminated conical shells subject to buckling load constraint is investigated. In the case of a laminated conical shell the thickness and the ply orientation (the design variables) are functions of the shell coordinates, influencing both the buckling load and its weight. These effects complicate the optimization problem consider...

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...