Improved Convex Underestimators and Hybrid Methods for Deterministic Global Optimization

知识内容：这项研究的主要目标是为各种化工过程设计、综合和操作问题中出现的全局优化问题开发新的理论、算法和计算技术。PI的目的是研究(I)两次连续可微约束非线性规划问题的一类新的改进的凸低估估计的发展，它将增强ABB方法，并将应用于各种相平衡、设计和综合问题；(Ii)ABB凸子泛函的一种新的剪切和拼接精化的理论和算法发展，它将导致新类型的Tigher凸低估估计；(Iii)几类非凸三角函数的新型三角凸低估估计的发展的理论和算法问题；以及(Iv)结合增强的ABB确定性全局优化框架和基于随机的方法的有益元素的新的HID全局优化方法的开发，以及它们的分布式计算实现，以及它们在合并和混合应用中出现的中型和大型非凸优化问题的应用。广泛的影响：通过在选修的非线性混合整数优化研究生课程中引入讲授材料和项目，以及必修的高级设计课程《化工过程设计、综合与优化》，将促进研究和教育的一体化。这项研究将扩大代表性不足群体的参与，因为它的目标是吸引研究生和本科高级论文水平的女性和少数族裔学生。这项工作的成果将通过在国内和国际会议上的陈述、学术参考的期刊出版物和我们的网页(http://titan.princeton.edu))向学术界和工业界的研究人员广泛传播，该网页将介绍方法、实施和结果。许多石化、化工、制药和服务/软件公司将受益于严格的全球优化方法的开发，这些方法可以解决工艺设计和运营中的重要问题。这可以更快地对市场需求做出反应，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.