Interior-Point Algorithms: Theories and Applications

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9522507 Ye The objective of this research is to develop and analyze interior-point algorithms and their variants for solving large-scale linear, quadratic, and nonlinear optimization problems that arise in production management and resource allocation. In the research, work will be performed to strengthen results obtained from prior research and explore new techniques for improving linear and nonlinear programming algorithms. The results of the research will be tested by solving actual industrial problems. Details of the research include (1) complexity analysis with the objective of developing complexity theory for linear programming (LP), (2) development of algorithms to extend LP-interior point algorithms to solve nonlinear optimization problems arising from engineering design and control, (3) decomposition and column generation for the development of interior point algorithms for solving large-scale, semi-infinite dimensional, and combinatorial optimization problems, and (4) implementation of the developed interior-point algorithms and development of public-domain computer programs based on the implementation. The findings and discoveries from this research will strengthen and improve theoretical results and practical performance of interior point algorithms. This will lead to the development of new efficient algorithms for a variety of optimization problems. Progress in the development of efficient algorithms for solving large-scale optimization problems improves the efficiency of manufacturing systems, communication networks, aircraft routing, multiple-flow operations, and resource planning. Strengthening research in this area will contribute to the national interest in industrial competitiveness and scientific knowledge.