| Summary: | 博士 === 國立成功大學 === 數學系應用數學碩博士班 === 92 === The purpose of this thesis is to present some results on linear programming on measure spaces (LPM). We shall discuss the conditions under which LPM is solvable and the optimal value of an LPM is equal to the optimal value of the dual problem;moreover, we present two algorithms for solving various LPM problems. Essentially, our approach extends the method introduced in cite{LaiWu94}. Besides, we use some examples to show that the proposed methods work for real. We also propose another approximation scheme to solve LPM.This scheme is a discretization method which finds a sequence of optimal solutions of corresponding linear semi-infinite programs, and which shows that the sequence of optimal solutions converges to an optimal solution of LPM. Finally, we implement these methods with providing some examples in the final section.
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