Constrained Nonlinear Problems

Numerical methods for solving general nonlinear constrained optimization problems are discussed in this chapter. A large number of methods and their variations are available in the literature for solving these problems. As is frequently the case with nonlinear problems, there is no single method that is clearly better than the others. Each method has its own strengths and weaknesses. The quest for a general method that works effectively for all types of problems continues. Most current journals and conferences on optimization contain new methods or refinements of existing methods for solving constrained nonlinear problems. A thorough review of all these developments is beyond the scope of this chapter. Instead, the main purpose of this chapter is to present the development of two methods that are generally considered among the best in their class, the ALPF (Augmented Lagrangian Penalty Function) method and the SQP (Sequential Quadratic Programming) method. For additional details refer to Fiacco [1983], Fiacco and McCormick [1968], Fletcher [1987], Gill, Murray, and Wright [1991], Gomez and Hennart [1994], McCormick [1983], Scales [1985], and Shapiro [1979].