A integral filter algorithm for unconstrained global optimization

• Published in: Applied mathematics and computation Vol. 184; no. 2; pp. 173 - 180
• Main Authors: Yang, Yongjian, Du, Xuewu, Li, Mingming
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.01.2007; Elsevier
• Subjects: Branch and bound; Calculus of variations and optimal control; Exact sciences and technology; Global optimization; Integral; Local search algorithm; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Sciences and techniques of general use; Integral; Global optimization; Local search algorithm; Branch and bound; Unconstrained optimization; Necessary and sufficient condition; Optimization method; Numerical method; Search algorithm; Applied mathematics; Objective function; Reliability; Deterministic algorithms; Mathematical programming
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2006.05.147

In this paper, making use of an integral inequality, a necessary and sufficient condition is given for a point to be a global minimizer. Based on the integral inequality, a novel integral-form algorithm is proposed for unconstrained global optimization. It is different from the other deterministic global search algorithm. Under mild conditions it is proved that, in theory, a global minimizer of the objective function can be certainly found by the presented algorithm. In order to indicate the efficiency and reliability of the method, four numerical examples are reported.