Nonconvexity in Chemical Process Optimization

化学工艺优化中的非凸性

• 批准号: 9312066
• 负责人: Angelo Lucia
• 金额: $ 9.71万
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-02-01 至 1996-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9312066&HistoricalAwards=false
• 关键词: Nonconvexity; Chemical; Process; Optimization

Abstract - Lucia - 9312066 Theoretically sound and reasonably reliable and efficient computer tools for finding local solutions to large chemical process optimization problems have been the focus of this PI's research. He has been working on developing a successive quadratic programming (SQP) method for nonlinearly constrained optimizations problems (an example of such problems are the design of separation units such as distillation columns). SQP methods are a very powerful class of methods for solving nonlinear programming problems, particularly those with strong nonlinear constraints. The single biggest weakness of SQP methods is the fact that iterative QP solutions can give directions of nondescent in the nonlinear program (NLP), even for convex quadratic programs. For this research project the PI plans to: A) Develop the theoretical framework for linear programming-based, asymmetric trust region methods that guarantee descent when the quadratic programming solution is not a descent direction. B) Conduct concomitant numerical studies directed at developing the necessary rules for adjusting the trust region size to guarantee both descent and convergence to a local Kuhn-Tucker point. C) Study the theoretical and computational implications of saddlepoint solutions to nonlinear programming algorithms. In addition, he plans to look at the general role of nonconvexity in quadratic programming by: 1) Conducting a numerical investigation and study of the relationship between nonconvexity and the inadequacy of current active set methods, the occurrence of constraint redundancy, the presence of multiplicity, nondescent, the requirement of starting point feasibility/infeasibility, projected definiteness, indefiniteness, and projected singularity. 2) Developing, in parallel, reliable and efficient algorithms that address these and other issues, including (a) new active set methods capable of handling projected indefiniteness with feasible or infeasible starting points, (b) preprocessing a lgorithms that can identify all smallest nontrivial redundant subsets of a given set of constrains, and (c) incorporating (b) into (a) when singularity is encountered. 3) Establishing theoretical foundations to both guide and support the algorithmic developments in 2) above.

摘要- Lucia - 9312066 理论上合理可靠和有效的计算机工具，寻找本地解决大型化工过程优化问题一直是这个PI的研究重点。 他一直致力于开发一种连续二次规划（SQP）方法，用于非线性约束优化问题（此类问题的一个例子是分离单元的设计，如蒸馏塔）。 SQP方法是求解非线性规划问题的一类非常强大的方法，特别是那些具有强非线性约束的问题。 SQP方法的最大缺点是迭代QP解可以给出非线性规划（NLP）的非下降方向，即使是凸二次规划。 对于本研究项目，PI计划：A）开发基于线性规划的非对称信赖域方法的理论框架，该方法在二次规划解不是下降方向时保证下降。 B）进行伴随的数值研究，旨在发展必要的规则来调整信赖域的大小，以保证下降和收敛到局部库恩-塔克点。 C）研究非线性规划算法鞍点解的理论和计算含义。 此外，他计划看看一般作用的非凸性在二次规划：1）进行数值调查和研究之间的关系非凸性和不足的现行活动集方法，发生的约束冗余，存在的多重性，非下降，要求的起点可行性/不可行性，预计明确性，不确定性，和预计奇异性。 2)并行开发解决这些问题和其他问题的可靠和有效的算法，包括（a）能够处理具有可行或不可行起点的投影不确定性的新的活动集方法，（B）预处理可以识别给定约束集合的所有最小非平凡冗余子集的ltax，以及（c）当遇到奇点时将（B）合并到（a）中。 3)建立理论基础，指导和支持上述2）中的算法开发。