Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
Optimal Quadratic Programming Algorithms: With Applications to Variational Inequalities
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发表时间：
2009-03
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通讯作者：
Zdenek Dostl
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作者：
Zdenek Dostl
解决复杂系统中的优化问题通常需要采用先进的数学技术。二次规划（QP）是一种允许在存在线性约束的情况下优化若干变量的二次函数的技术。QP问题出现在电气工程、农业规划和光学等不同领域。鉴于其广泛的适用性，对二次规划的全面理解几乎在每个科学领域都是一个宝贵的资源。最优二次规划算法提出了最近开发的解决大QP问题的算法。该演示文稿的重点是算法，在某种意义上是最佳的，即，它们可以解决重要的问题，而成本与未知数的数量成正比。对于每一个算法，书中详细介绍了它的经典前辈，描述了它的缺点，介绍了改进其性能的修改，并通过数值实验证明了这些改进。这本独立的专著可以作为研究生和研究人员的二次规划的介绍性文本。此外，由于许多非线性问题的解决方案可以减少到一系列QP问题的解决方案，它也可以用来作为一个方便的介绍非线性规划。读者需要有一个基本的知识微积分在几个变量和线性代数。
Solving optimization problems in complex systems often requires the implementation of advanced mathematical techniques. Quadratic programming (QP) is one technique that allows for the optimization of a quadratic function in several variables in the presence of linear constraints. QP problems arise in fields as diverse as electrical engineering, agricultural planning, and optics. Given its broad applicability, a comprehensive understanding of quadratic programming is a valuable resource in nearly every scientific field. Optimal Quadratic Programming Algorithms presents recently developed algorithms for solving large QP problems. The presentation focuses on algorithms which are, in a sense optimal, i.e., they can solve important classes of problems at a cost proportional to the number of unknowns. For each algorithm presented, the book details its classical predecessor, describes its drawbacks, introduces modifications that improve its performance, and demonstrates these improvements through numerical experiments. This self-contained monograph can serve as an introductory text on quadratic programming for graduate students and researchers. Additionally, since the solution of many nonlinear problems can be reduced to the solution of a sequence of QP problems, it can also be used as a convenient introduction to nonlinear programming. The reader is required to have a basic knowledge of calculus in several variables and linear algebra.