Optimality Conditions

Abstract

This chapter deals with mathematical conditions that must be satisfied by the solution of an optimization problem. A thorough understanding of the concepts presented in this chapter is a prerequisite for understanding the material presented in later chapters. The subject matter of this chapter is quite theoretical and requires use of sophisticated mathematical tools for rigorous treatment. Since the book is not intended to be a theoretical text on mathematical optimization, this chapter is kept simple by appealing to intuition and avoiding precise mathematical statements. Thus, it is implicit in the presentation that all functions are well behaved and have the necessary continuity and differentiability properties. The book by Peressini, Sullivan and Uhl, Jr. [1988] is recommended for those interested in a mathematically rigorous, yet very readable, treatment of most of the concepts presented in this chapter. More details can also be found in Beveridge, Gordon, and Schechter [1970], Jahn [1996], Jeter [1986], McAloon and Tretkoff [1996], Pierre and Lowe [1975], and Shor [1985].