Abstract
We consider a convex multiplicative programming problem of the form
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where X is a compact convex set of ℝn and f 1, f 2 are convex functions which have nonnegative values over X.
Using two additional variables we transform this problem into a problem with a special structure in which the objective function depends only on two of the (n+2) variables. Following a decomposition concept in global optimization we then reduce this problem to a master problem of minimizing a quasi-concave function over a convex set in ℝ2 2. This master problem can be solved by an outer approximation method which requires performing a sequence of simplex tableau pivoting operations. The proposed algorithm is finite when the functions f i, (i=1, 2) are affine-linear and X is a polytope and it is convergent for the general convex case.
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Partly supported by the Deutsche Forschungsgemeinschaft Project CONMIN.
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Van Thoai, N. A global optimization approach for solving the convex multiplicative programming problem. J Glob Optim 1, 341–357 (1991). https://doi.org/10.1007/BF00130830
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DOI: https://doi.org/10.1007/BF00130830