Global minimization of a generalized convex multiplicative function

Konno, Hiroshi; Kuno, Takahito; Yajima, Yasutoshi

doi:10.1007/bf01096534

Cited by 82 publications

(45 citation statements)

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“…Konno et al construct an outer approximation algorithm based on the above method and report the results of its computational experiments in [22]. In case each of f;'s is either convex quadratic or affine, and X is a polytope, they confirmed that the number of cuts generated in the course of computation depends only upon p.…”

Section: Minimization Of a Sum Of Convex Multiplicative Functionsmentioning

confidence: 87%

Multiplicative Programming Problems

Konno

Kuno

1995

Nonconvex Optimization and Its Applications

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Abstract. This chapter reviews recent algorithmic developments in multiplicative programming. The multiplicative programming problem is a class of minimization problems containing a product of several convex functions either in its objective or in its constraints. It has various practical applications in such areas as microeconomics, geometric optimization, multicriteria optimization and so on. A product of convex functions is in general not (quasi)convex, and hence the problem can have multiple local minima. However, some types of multiplicative problems can be solved in a practical sense. The types to be discussed in this chapter are minimization of a product of p convex functions over a convex set, minimization of a sum of p convex multiplicative functions, and minimization of a convex function subject to a constraint on a product of p convex functions. If p is less than four or five, it is shown that parametric simplex algorithms or global optimization algorithms work very well for these problems.

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Section: Minimization Of a Sum Of Convex Multiplicative Functionsmentioning

confidence: 87%

Multiplicative Programming Problems

Konno

Kuno

1995

Nonconvex Optimization and Its Applications

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“…It has been established in [15] that the sequence ( k , k ) converges to the global minimum of G(, ) over ⍀.…”

Section: Algorithmmentioning

confidence: 99%

“…, p) are nonnegative convex functions and X ʚ ‫ޒ‬ n is a compact convex set. To the authors' knowledge, the only reported computational results on the algorithm is the one reported in [15], where f is a nonconvex quadratic function. We will show in this paper that this general approach can lead to practical algorithms for solving (1) and (2) for p up to four.…”

Section: Introductionmentioning

confidence: 96%

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Minimizing sums and products of linear fractional functions over a polytope

Konno

Yamashita

1999

Naval Research Logistics

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“…Later, Falk and Palocsay [10] developed an image space algorithm suitable for globally solving the same problem when p ≥ 2. Since then, several algorithms using outer approximation, branch and bound, or parametric linear programming have been developed for solving various sums of ratios problems, many of which are special cases of problem (P) [7,13,14,16,20,21].…”

Section: Introductionmentioning

confidence: 99%