BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jean Pauphilet (London Business School) DTSTART:20200630T183000Z DTEND:20200630T190000Z DTSTAMP:20260423T021826Z UID:DOTs/20 DESCRIPTION:Title: A Unified Approach to Mixed-Integer Optimization: Nonlinear Formulations and Scalable Algorithms\nby Jean Pauphilet (London Business School) as pa rt of Discrete Optimization Talks\n\n\nAbstract\nWe propose a unified fram ework to address a family of classical mixed-integer optimization problems with semicontinuous decision variables\, including network design\, facil ity location\, unit commitment\, sparse portfolio selection\, binary quadr atic optimization\, sparse principal component analysis\, and sparse learn ing problems. These problems exhibit logical relationships between continu ous and discrete variables\, which are usually reformulated linearly using a big-M formulation. In this work\, we challenge this longstanding modeli ng practice and express the logical constraints in a non-linear way. By im posing a regularization condition\, we reformulate these problems as conve x binary optimization problems\, which are solvable using an outer-approxi mation procedure. Numerically\, we establish that a general-purpose strate gy\, combining cutting-plane\, first-order\, and local search methods\, so lves these problems faster and at a larger scale than MICO solvers. For in stance\, our approach successfully solves network design problems with 100 s of nodes and provides solutions up to 40% better.\n LOCATION:https://researchseminars.org/talk/DOTs/20/ END:VEVENT END:VCALENDAR