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UBC Theses and Dissertations

Necessary conditions for a solution of a non-linear programming problem Lee, Linda May

Abstract

The conditions required for a solution of general non-linear programming problems of the form min{f(x): x є X, g(x) ≤ 0, h(x)=0}; where f is called the objective function, g the inequality constraint and. h the equality constraint, are presented in this thesis. The following cases are studied: (1) X, a finite dimensional space; f, a real valued function; and g and h finite dimensional vector functions. (2) X, an infinite dimensional space; f, a real valued function; and g and h either finite or infinite dimensional vector functions. An application of this type of problem to optimal control will be given and the recent developments in this area will be discussed.

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