| Summary: | 博士 === 元智大學 === 工業工程研究所 === 88 === This dissertation studies certain nonlinear programming problems and its algorithms. We divided it roughly into two categories. The first category states a necessary and sufficient optimality condition for a local optimal solution to be global one, providing various numerical routines with these conditions as a stopping criteria to yield a global solution in nonconvex quadratic programming problems with equal quadratic constraints. Based on the condition, for a KKT point given, if it is not global then it is possible to find an improved feasible point. By this point, we develop an algorithm to solve it.
In the second category, we focus on the fractional programming problems, especially in linear fractional programming and its composite problems, and describe them in two parts. In part one, we develop two fast, effective linear-time iterative algorithms for searching the global minimum of linear fractional programming problems without constraints, arised from fuzzy weighted average (FWA) problems. Completeness as well as convergence of algorithm are discussed.
The second part will study one type of nonlinear programming problems whose objective is the sum of linear ratios (SLR) with linear constraints. We propose a heuristic simplex-like algorithm to solve this problem and develop the tableau algebra of algorithm as well. Furthermore, we propose a conjecture to claim this solution obtained by our algorithm is not only a KKT point but a global one.
KEY WORDS. nonconvex quadratic programmin, KKT point, linear fractional programming, fuzzy weighted average, sum of ratios of linear ratios, parametric method, simplex-like algorithm.
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