SFU Operations Research Seminars: Tanmaya Karmarkar
Date

Topic
Tensor Optimization and Applications
Speakers
Details
First example of applying tensor optimization to combinatorial problems was shown in IPCO 1992: pages 406420. We improve and strengthen those results in several ways and obtain computational results on three problems â€“ graph partitioning, satisfiability and analysis of counterexamples related to Hilbertâ€™s 17th problem. For this we created a mixed symbolicnumeric model formulation package which facilitates definition of objective function, equality and inequality constraints and definition of new dependent variables. For discrete problems certain inequalities valid at candidate solutions are dynamically incorporated in the iterations of the continuous optimization algorithm based on underlying nonNewtonian geometry of the interiorpoint space. For graph partitioning we obtain optimal solutions including proof of optimality. For satisfiability problem we either find the satisfiable assignment or construct and output proof of unsatisfiability. For Hilbertâ€™s 17th problem we analyse concrete examples whose nonnegativity has been stablished to be not provable using sums of the squares expressions valid in RN. However, for these counterexamples, we construct nonnegativity proofs by computationally constructing sums of squares expressions valid on certain subvarieties of RN The same modeling package mentioned above is used to post process the solver output into symbolic proofs of optimality or infeasibility.
Additional Information
Time: 3.30pm  4.30pm Pacific
Location: ASB 10908 (UBCO hosted)
Tanmaya Karmarkar, UBC Okanagan
This is a Past Event
Event Type
Scientific, Seminar
Date
January 19, 2023
Time

Location