ABSTRACT
This chapter discusses conditions that are necessary and conditions that are sometimes sufficient for a relative extreme value of a real valued function of several real variables which satisfy various types of constraints. It also discusses the Kuhn-Tucker theorem which establishes the relationship that exists between solutions of the type of problem just mentioned and the solutions of the corresponding saddle-point problem of the related Lagrangran function. The chapter explains necessary and sufficient conditions for a maximum value of a differentiable concave function of several real variables subject to inequality constraints. It illustrates the application of the Kuhn-Tucker conditions to the quadratic programming problem resulting in a restatement of the problem as a linear complementarity problem. It is necessary to recall Lemke's algorithm for solving a linear complementarity problem. The chapter also illustrates an example of the algorithm.
