Review of some Constrained Optimization Schemes
Jonnalagadda Srinivas · 2019
This chapter summarizes the existing important constrained optimization schemes. It reviews some direct solution schemes including complex search, random search and method of feasible directions, and their performance in terms of accuracy, computational requirements and time at par with commonly used modern heuristic algorithms. It presents a review of a few techniques of obtaining optimum solutions for constrained nonlinear programming problems and attempts to identify their benefits and difficulties over heuristic methods such as simulated annealing. The chapter explains a few methods to handle multi-objective optimization problems. In direct search methods for constrained minimization, the structure of constraints is employed. The main advantage of such methods is handling of discontinuous and non-differentiable functions. In indirect approaches, the constrained nonlinear problem is converted into an equivalent unconstrained one. When a constraint is violated, the objective function is penalized by the extent of its violation. There are two penalty methods: interior penalty methods and exterior penalty methods.