NP-hardness of deciding convexity of quartic polynomials and related problems

We show that unless P = NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the comple...

Celý popis

Uložené v:

Podrobná bibliografia
Vydané v:	Mathematical programming Ročník 137; číslo 1-2; s. 453 - 476
Hlavní autori:	Ahmadi, Amir Ali, Olshevsky, Alex, Parrilo, Pablo A., Tsitsiklis, John N.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Berlin/Heidelberg Springer-Verlag 01.02.2013 Springer Nature B.V
Predmet:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorics Complexity Convex analysis Convexity Full Length Paper Mathematical and Computational Physics Mathematical Methods in Physics Mathematical programming Mathematics Mathematics and Statistics Mathematics of Computing Multivariate analysis Numerical Analysis Optimization Polynomials Studies System theory Theoretical 90C25 Convex programming 90C60 Abstract computational complexity for mathematical programming problems 68Q25 Analysis of algorithms & problem complexity
ISSN:	0025-5610, 1436-4646
On-line prístup:	Získať plný text
Tagy:	Pridať tag Žiadne tagy, Buďte prvý, kto otaguje tento záznam!

Buďte prvý, kto okomentuje tento záznam!