Improved Convex Underestimators and Hybrid Methods for Deterministic Global Optimization

知识内容：本研究的主要目标是开发新的理论，算法和计算技术的全局优化问题，出现在各种化学工程过程的设计，合成和操作问题。PI的目的是研究（i）开发一类新的改进的凸低估器用于二次连续可微约束非线性规划问题，这将增强aBB方法，并将应用于各种相平衡，设计和综合问题;（二）理论和算法的发展，一种新的切割和拼接细化的aBB凸子功能，将导致新类型的紧凸低估;（iii）理论和算法问题的发展新的三角凸低估几类非凸三角函数;以及（iv）新的aBB全局优化方法的开发，其将增强的aBB确定性全局优化框架的有益元素与基于随机的方法及其分布式计算实现相结合，以及它们在池化和混合应用中出现的中型和大型非凸优化问题中的应用。研究和教育的整合将通过在非线性混合优化选修研究生课程的讲座材料和项目的介绍，以及所需的顶点高级设计课程设计，化工过程的综合与优化。 这项研究将扩大代表性不足群体的参与，因为它的目的是吸引研究生和本科毕业论文的女生和少数民族学生。工作结果将通过在国内和国际会议上的介绍、学术期刊出版物和我们的网页（http：//www.example.com）向学术界和工业界的研究人员广泛传播，该网页将介绍各种方法、实施情况和结果。titan.princeton.edu 许多石化、化工、制药和服务/软件公司将受益于严格的全局优化方法的开发，这些方法可以解决工艺设计和操作中的重要问题。这可以更快地对市场需求作出反应，从而更有效地利用加工设施，这对美国经济有直接好处。

Intellectual Content: The primary objective of this research is to develop novel theoretical, algorithmic and computational techniques for global optimization problems that arise in a variety of chemical engineering process design, synthesis and operations problems. It is the PI's intention to investigate (i) the development of a new class of improved convex underestimators for twice-continuously differentiable constrained nonlinear programming problems which will enhance the aBB approach and will be applied in a variety of phase equilibrium, design and synthesis problems; (ii) the theoretical and algorithmic development of a novel cut and splice refinement of the aBB convex subfunctional that will result in new types of tigher convex underestimators; (iii) the theoretical and algorithmic issues for the development of novel trigonometric convex underestimators for several classes of nonconvex trigonometric functions; and (iv) the development of new hydrid global optimization methods which combine the beneficial elements of the enhanced aBB deterministic global optimization framework with stochastic based approaches, and their distributed computing implementations, and their applications to medium and large-scale nonconvex optimization problems that arise in pooling and blending applications.Broader Impact: The integration of research and education will be enhanced through the introduction of lecture material and projects in the elective graduate course on Nonlinear Mixed Integer Optimization, and the required capstone senior design course Design, Synthesis and Optimization of Chemical Processes. The research will broaden the participation of underrepresented groups since it will aim at attracting female and minority students at the graduate level and the undergraduate senior theses level. The results of the work will be broadly disseminated to researchers in academia and industry through presentations at domestic and international meetings, scholarly refereed journal publications and through our web page (http://titan.princeton.edu) which will describe the approaches, implementations and results. Many petrochemical, chemical, pharmaceutical and services/software companies will benefit by the development of rigorous global optimization methods that can address important problems in process design and operations. This can lead to faster response to the market demands, and hence more efficient use of the processing facilities, which has direct benefit on the US economy.