Geometry of exactness of moment-SOS relaxations for polynomial optimization

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00383696" target="_blank" >RIV/68407700:21230/25:00383696 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s11590-025-02202-8" target="_blank" >https://doi.org/10.1007/s11590-025-02202-8</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11590-025-02202-8" target="_blank" >10.1007/s11590-025-02202-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Geometry of exactness of moment-SOS relaxations for polynomial optimization

Popis výsledku v původním jazyce

The moment-SOS (sum of squares) hierarchy is a powerful approach for solving approximately and globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if solving the relaxation actually solves the POP globally. In this note, we study the geometry of the exactness cone, defined as the set of polynomial objective functions for which the relaxation is exact. Generalizing previous foundational work on quadratic optimization on real varieties, we prove by elementary arguments that the exactness cones are unions of semidefinite representable cones monotonically embedded for increasing relaxation order.

Název v anglickém jazyce

Geometry of exactness of moment-SOS relaxations for polynomial optimization

Popis výsledku anglicky

The moment-SOS (sum of squares) hierarchy is a powerful approach for solving approximately and globally non-convex polynomial optimization problems (POPs) at the price of solving a family of convex semidefinite optimization problems (called moment-SOS relaxations) of increasing size, controlled by an integer, the relaxation order. We say that a relaxation of a given order is exact if solving the relaxation actually solves the POP globally. In this note, we study the geometry of the exactness cone, defined as the set of polynomial objective functions for which the relaxation is exact. Generalizing previous foundational work on quadratic optimization on real varieties, we prove by elementary arguments that the exactness cones are unions of semidefinite representable cones monotonically embedded for increasing relaxation order.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EH22_008%2F0004590" target="_blank" >EH22_008/0004590: Robotika a pokročilá průmyslová výroba</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Optimization Letters

ISSN

1862-4472

e-ISSN

1862-4480

Svazek periodika

19

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

10

Strana od-do

1239-1248

Kód UT WoS článku

001484444800001

EID výsledku v databázi Scopus

2-s2.0-105004438835