Novel Nonmonotone Line-Search Method for Constrained Nonlinear Programming: Algorithmic Concepts and Preliminary Computational Studies

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• 作者：Vassilios S. Vassiliadis ; Intan S. Ahamad ; Raú ; l Conejeros
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2006
• 出版时间：December 6, 2006
• 年：2006
• 卷：45
• 期：25
• 页码：8270 - 8281
• 全文大小：224K
• 年卷期：v.45,no.25(December 6, 2006)
• ISSN：1520-5045

文摘

A new nonmonotone line-search procedure is presented for the generally constrained case of nonlinearprogramming problems. The new algorithm is based on the use of standard penalty methods for the definitionof merit functions used during line search to find the next iterate in algorithms generating a search directioniteratively. The key concept is the discretization of the penalty parameter used over a finite range of ordersof magnitude and the provision of a memory list for each such order, as in standard nonmonotone line-searchprocedures used for unconstrained optimization. Nonmonotonicity helps in escaping from local minima, whilethe discretized penalty parameters overcome the difficulties in choosing a penalty parameter that varies, buthaving the same definition as the problem while not underpenalizing the constraints to arrive at the desiredKKT point. An implementation within a customized logarithmic barrier algorithm for bounds' handling ispresented with capabilities for very large scale applications; the algorithm uses exact first and second derivativeinformation, derived symbolically, and the search direction is generated by solution of the Lagrange-Newtonequations. The case studies presented demonstrate the capabilities of the new line-search procedure, andcomparisons with other methods are discussed. It is noted that we found a significantly better solution in casestudy 5. The new nonmonotone line-search procedure is, at present, a heuristic and from the computationalpoint of view: future work will focus on the investigation of both the theoretical properties of the methodand new implementation aspects.