On boundedness of (quasi-)convex integer optimization problems |
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Authors: | Wies?awa T Obuchowska |
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Institution: | (1) Department of Mathematics, East Carolina University, Greenville, NC 27858, USA |
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Abstract: | In this paper we are concerned with the problem of boundedness and the existence of optimal solutions to the constrained integer
optimization problem. We present necessary and sufficient conditions for boundedness of either a faithfully convex or quasi-convex
polynomial function over the feasible set contained in , and defined by a system of faithfully convex inequality constraints and/or quasi-convex polynomial inequalities. The conditions
for boundedness are provided in the form of an implementable algorithm, terminating after a finite number of iterations, showing
that for the considered class of functions, the integer programming problem with nonempty feasible region is unbounded if
and only if the associated continuous optimization problem is unbounded. We also prove that for a broad class of objective
functions (which in particular includes polynomials with integer coefficients), an optimal solution set of the constrained
integer problem is nonempty over any subset of . |
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Keywords: | Convex constrained integer programs Boundedness Existence of optimal solutions |
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