NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program

Deepak Ponvel Chermakani

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arXiv · 1212.5097

NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program

Deepak Ponvel Chermakani

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Abstract

We convert, within polynomial-time and sequential processing, an NP-Complete Problem into a real-variable problem of minimizing a sum of Rational Linear Functions constrained by an Asymptotic-Linear-Program. The coefficients and constants in the real-variable problem are 0, 1, -1, K, or -K, where K is the time parameter that tends to positive infinity. The number of variables, constraints, and rational linear functions in the objective, of the real-variable problem is bounded by a polynomial function of the size of the NP-Complete Problem. The NP-Complete Problem has a feasible solution, if-and-only-if, the real-variable problem has a feasible optimal objective equal to zero. We thus show the strong NP-hardness of this real-variable optimization problem.

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BibTeX RIS

Deepak Ponvel Chermakani. 2012-12-15. NP-Hardness of optimizing the sum of Rational Linear Functions over an Asymptotic-Linear-Program. https://arxiv.org/abs/1212.5097

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