Abstract
This paper addresses the minimization of the product ofp convex functions on a convex set. It is shown that this nonconvex problem can be converted to a concave minimization problem withp variables, whose objective function value is determined by solving a convex minimization problem. An outer approximation method is proposed for obtaining a global minimum of the resulting problem. Computational experiments indicate that this algorithm is reasonable efficient whenp is less than 4.
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This research was partly supported by Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Grant No. (C)03832018 and (C)04832010.
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Kuno, T., Yajima, Y. & Konno, H. An outer approximation method for minimizing the product of several convex functions on a convex set. J Glob Optim 3, 325–335 (1993). https://doi.org/10.1007/BF01096774
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DOI: https://doi.org/10.1007/BF01096774