Optimization Methods

Abstract

The optimization programs tested in the scope of this report realize various mathematical algorithms and the intention of this chapter is to give a rough sketch of their concepts. In particular, we describe the fundamental mathematical methods without any attempt to be complete and give references where the interested reader can find further details, convergence results, etc., Since all programs require auxiliary routines for special types of subproblems, we begin the chapter with reviews of line-search, quadratic programming, and unconstrained optimization algorithms. Since these methods are often ignored in the corresponding user instructions of the constrained nonlinear programming codes, we explain them more comprehensively and present implementation details together with some sources of computer programs. Subsequently, the methods for solving the general constrained problem (1) which are realized numerically by the submitted optimization programs are described. They consist of penalty, multiplier, quadratic approximation, generalized reduced gradient algorithms, and a special method developed by Robinson. More details and some information about their individual implementation are given in Chapter III.