Mathematical Sciences: Numerical Techniques in Control and Optimization

解决最优化问题的数值方法将 开发和分析。 研究将集中在：a）。 的 对偶有效集算法是由 解决数学规划的首席研究员 问题，将在线性规划的背景下进行研究 二次规划和极大极小 B）。 增广拉格朗日量 数学规划问题的型算法 将 以适合大规模的方式重新制定 优化. （c）。 最优逼近技术 问题，将扩展到处理状态约束。主要 重点将放在应用这些优化技术 研究雷暴产生的电场

Numerical methods for solving optimization problems will be developed and analyzed. The research will focus on: a). The Dual Active Set Algorithm, a new algorithm developed by the principal investigator for solving mathematical programming problems, will be studied in the context of linear programming quadratic programming and minimax. b). An augmented Lagrangian type algorithm for mathematical programming problems will be reformulated in a way that is appropriate for large scale optimization. c). Approximation techniques for optimal problems, will be extended to handle state constraints. The main emphasis will be placed on applying these optimization techniques in the study of electric fields generated in thunderstorms.