BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tanmaya Karmarkar (UBC-O hosted) (UBC Okanagan) DTSTART:20230119T233000Z DTEND:20230120T003000Z DTSTAMP:20260513T193650Z UID:SFUOR/11 DESCRIPTION:Title: T ensor Optimization and Applications\nby Tanmaya Karmarkar (UBC-O hoste d) (UBC Okanagan) as part of PIMS-CORDS SFU Operations Research Seminar\n\ nLecture held in ASB 10908.\n\nAbstract\nFirst example of applying tensor optimization to combinatorial problems was shown in IPCO 1992: pages 406-4 20. We improve and strengthen those results in several ways and obtain com putational results on three problems – graph partitioning\, satisfiabili ty and analysis of counterexamples related to Hilbert’s 17th problem.\n\ nFor this we created a mixed symbolic-numeric model formulation package wh ich facilitates definition of objective function\, equality and inequality constraints and definition of new dependent variables.\n\nFor discrete pr oblems certain inequalities valid at candidate solutions are dynamically i ncorporated in the iterations of the continuous optimization algorithm bas ed on underlying non-Newtonian geometry of the interior-point space.\n\nFo r graph partitioning we obtain optimal solutions including proof of optima lity. For satisfiability problem we either find the satisfiable assignment or construct and output proof of unsatisfiability.\n\nFor Hilbert’s 17t h problem we analyse concrete examples whose non-negativity has been stabl ished to be not provable using sums of the squares expressions valid in RN . However\, for these counterexamples\, we construct non-negativity proofs by computationally constructing sums of squares expressions valid on cert ain sub-varieties of RN The same modeling package mentioned above is used to post process the solver output into symbolic proofs of optimality or in feasibility.\n LOCATION:https://researchseminars.org/talk/SFUOR/11/ END:VEVENT END:VCALENDAR