%0 Conference Paper %F Oral %T Nested branch-and-bound algorithm for minmax problem and constraints with quantifiers %+ Equipe Models and AlgoriThms for pRocessIng and eXtracting information (Lab-STICC_MATRIX) %+ École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne) %+ Groupe d’études et de recherche en analyse des décisions (GERAD) %A Ninin, Jordan %A Monnet, Dominique %A Clement, Benoit %< avec comité de lecture %B EUROPT 2021, the 18th international workshop on continuous optimization %C Toulouse, France %8 2021-07-07 %D 2021 %Z Computer Science [cs]/Operations Research [cs.RO] %Z Mathematics [math]/Optimization and Control [math.OC] %Z Computer Science [cs]/Automatic Control EngineeringConference papers %X We consider global optimization problems of a minmax function subject to constraints with quantifiers. The goal is to minimize over x the maximum over y of f(x,y), and constraints with quantifiers must be satisfied for a set of value (for all y in S). We present an algorithm to address this non-smooth objective function and the constraints with quantifiers in the same way. Our approach is a set-valued method based on two nested branch-and-bound algorithm, using interval analysis. This problem arises in structured robust control, semi-infinite optimization or minmax optimization. %G English %L hal-03474825 %U https://hal.science/hal-03474825 %~ UNIV-BREST %~ INSTITUT-TELECOM %~ ENSTA-BRETAGNE %~ CNRS %~ UNIV-UBS %~ ENSTA-BRETAGNE-STIC %~ INSMI %~ ENIB %~ LAB-STICC %~ TDS-MACS %~ INSTITUTS-TELECOM %~ TEST-HALCNRS %~ LAB-STICC_MATRIX %~ LAB-STICC_DMID