Progress on polynomial optimization

Abstract: In this talk I will describe ongoing work on polynomial optimization problems (POPs), from a discrete optimization perspective, that is to say, using techniques motivated by mixed-integer programming. In particular I will primarily focus on methods for producing solutions, and on the feasibility of such solutions. The current "king of the hill" for computing solutions to POPs are filter methods relying on logarithmic barrier algorithms, implemented in codes such as IPOPT or KNITRO. Instead we will focus on techniques based on integer programming -- such techniques are not yet competitive with the solvers just mentioned, but may soon yield competitive algorithms.

If time permits, I will also describe joint work (with Chen Chen and Gonzalo Munoz) on techniques for obtaining lower bounds for POPs based on classical cutting-plane techniques, such as intersection cuts.

game theorymachine learningmathematical softwarecomputer science theorycombinatoricsoptimization and control

Audience: researchers in the topic

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Mixed Integer Programming Workshop 2021

Series comments: The 18th Mixed Integer Programming Workshop will be held online on May 24-27, 2021.

It will feature 21 distinguished invited speakers covering most aspects of Mathematical Optimization, an interactive, gamified MIP student poster session with 50 posters, and a casual business meeting.

Registration is free of charge. Register here: fico.zoom.us/webinar/register/2416186463858/WN_DVLhGOToQkKyvKYPiA4cQw

Find the website of MIP2021 at sites.google.com/view/mipworkshop2021/.

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