Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming
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DOI：
10.1007/978-1-4757-3532-1
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发表时间：
2002-10
影响因子：
2.9
通讯作者：
Mohit Tawarmalani;N. Sahinidis
中科院分区：
文献类型：
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作者：
Mohit Tawarmalani;N. Sahinidis
对约束优化的兴趣起源于简单的线性规划模型，因为它是实用的，并且可能是当时唯一可计算的模型。约束线性优化模型很快被许多应用领域所采用，并且可能是撰写本文时在运筹学和管理科学中使用最广泛的数学模型。然而，建模者发现，线性假设在表达经济学、金融、商业、通信、工程设计、计算生物学和其他经常需要在优化模型中使用非线性表达式和离散变量的领域中的现实世界现象和问题时过于严格。线性规划模型的这两个扩展都是np困难的，因此代表了非常具有挑战性的问题。从好的方面来看，最近算法和计算技术的进步使得重新审视这些问题成为可能，希望在合理的计算时间内解决实际相关的问题。求解非线性规划的最初尝试集中于在凸性假设下保证全局的局部优化方法的发展。另一方面，整数规划的发展集中在确保全局最优的方法上。本书的目的是结合解决非线性和整数规划模型的进步，并在混合整数非线性规划（minlp）的更一般框架中开发新的结果，目的是为minlp设计实际有效的全局优化算法。
Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.