GLODS: Global and Local Optimization using Direct Search

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• 作者：A. L. Custódio ; J. F. A. Madeira
• 关键词：Global optimization ; Multistart strategies ; Direct ; search methods ; Pattern ; search methods ; Nonsmooth calculus ; 90C56 ; 90C26 ; 90C30
• 刊名：Journal of Global Optimization
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：62
• 期：1
• 页码：1-28
• 全文大小：881 KB
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• 作者单位：A. L. Custódio (1)
  J. F. A. Madeira (2) (3)
  
  1. Department of Mathematics, FCT-UNL-CMA, Quinta da Torre, 2829-516?, Caparica, Portugal
  2. IDMEC, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1040-001?, Lisbon, Portugal
  3. Department of Mathematics, ISEL, Rua Conselheiro Emídio Navarro, 1, 1959-007?, Lisbon, Portugal
  
• 刊物类别：Business and Economics
• 刊物主题：Economics
  Operation Research and Decision Theory
  Computer Science, general
  Real Functions
  Optimization
  
• 出版者：Springer Netherlands
• ISSN：1573-2916

文摘

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.