Improved Convex Underestimators and Hybrid Methods for Deterministic Global Optimization

智力内容：本研究的主要目标是为各种化学工程过程设计、合成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打算研究(i)开发一类新的改进的凸低估器，用于两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；（ii）对aBB凸子泛函进行新的切割和拼接改进的理论和算法开发，这将产生新型的更严格的凸低估器；（iii）针对几类非凸三角函数开发新的三角凸低估器的理论和算法问题；（iv）开发新的混合全局优化方法，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相结合，以及它们的分布式计算实现，以及它们在池化和混合应用中出现的中型和大规模非凸优化问题中的应用。更广泛的影响：通过在研究生选修课程《非线性混合整数优化》和必修的高级设计课程《化学过程的设计、合成与优化》中引入讲座材料和项目，将加强研究与教育的整合。这项研究将扩大代表性不足的群体的参与，因为它的目的是在研究生阶段和本科高级论文阶段吸引女性和少数民族学生。这项工作的结果将通过在国内和国际会议上的演讲、学术评审期刊出版物和我们的网页（http://titan.princeton.edu）广泛传播给学术界和工业界的研究人员，该网页将描述方法、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发展，这些方法可以解决过程设计和操作中的重要问题。这可以更快地响应市场需求，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.