Title: Homogeneous scalarization for a class of multi-objective polynomial optimization problems
Speaker: Dr. Sujeet Kumar Singh.
Date, Time: 23rd September 2019, 10.30 AM - 11.30 AM
Venue: IEOR Seminar Hall, 2nd Floor, IEOR Building.
Abstract: In this talk multi-objective polynomial optimization problem with fractional objectives is considered. Further a suitable homogeneous change of variables is introduced to transform the fractional objectives and constraints into homogeneous polynomials. Then the equivalency of the former and the latter problems is established. The theoretical correctness of the proposed approach of homogeneously scalarizing the multi-objective polynomials into a homogeneous single objective polynomial is established and the topological properties of the solution set are studied. Furthermore, we show that a general class of non-smooth polynomial optimization problems can be reduced to a single degree homogeneous multi-objective polynomial optimization problem, using the concept of dual positively homogeneous optimization. Moreover, it is observed that the reduced problem is a concave maximization problem.
About the Speaker: Dr. Sujeet Kumar Singh was working as a research fellow at The Logistics Institute-Asia Pacific, National University of Singapore for the last 3 years under Prof. Mark Goh. During this period, he has worked with several industrial projects related to logistics, reverse logistics and vehicle routing problems. Beside the assigned projects, he has worked on multi objective and polynomial optimization problems with applications in supply chain. His Ph.D. work at IIT Roorkee under the supervision of Prof. Shiv Prasad Yadav, involved select studies in transportation problems, multi objective optimization and modeling industrial problems in uncertain environment. Dr. Sujeet plans to continue working with mathematical optimization problems including convex and polynomial optimization with applications to real-world problems and will try to use the SOS (sum of squares) theory extensively.