Mathematical Sciences: Numerical Techniques in Control and Optimization

将开发和分析求解优化问题的数值方法。研究将集中在：a)。本文将在线性规划、二次规划和极大极小的背景下，研究由主要研究者开发的一种求解数学规划问题的新算法——对偶活动集算法。b)。数学规划问题的增广拉格朗日算法将以一种适合大规模优化的方式重新表述。c)。最优问题的近似技术，将扩展到处理状态约束。重点将放在这些优化技术在雷暴电场研究中的应用。

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.