On the complexity of testing attainment of the optimal value in nonlinear optimization

We prove that unless P = NP , there exists no polynomial time (or even pseudo-polynomial time) algorithm that can test whether the optimal value of a nonlinear optimization problem where the objective and constraints are given by low-degree polynomials is attained. If the degrees of these polynomial...

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Bibliographic Details
Published in:	Mathematical programming Vol. 184; no. 1-2; pp. 221 - 241
Main Authors:	Ahmadi, Amir Ali, Zhang, Jeffrey
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2020 Springer Nature B.V
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Coercivity Combinatorics Full Length Paper Job shops Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Polynomials Semidefinite programming Theoretical Semidefinite programming 90C30 Frank–Wolfe type theorems Archimedean quadratic modules Existence of solutions in mathematical programs 90C60 Computational complexity Coercive polynomials
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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