Collaborative Proposal: Scaling up MINLPs via Branch-and-Bound and First Order Methods with applicat
Abstract
Collaborative Proposal: Scaling up MINLPs via Branch-and-Bound and First Order Methodswith applications to Structured Statistical Le,arning? PIs: Dey and Mazumder? Approved for Public ReleaseIn this project we investigate new methods and algorithms for solving larg,e-scale mixed integer nonlinear programs (MINLPs), inspired by key problems arising in structured statistical learning with combinat,orial structures. Indeed, many problems in statistical learning can be posed as constrained optimization tasks involving both contin,uous and discrete variables, posing outstanding challenges from an optimization perspective. Recent research has shown the promise o,f mixedinteger optimization for addressing some of these problems. However, as constrained statistical learning problems become main,stream, and datasets grow big and wide, there is an urgent need to create principled optimization methodology to reliably solve MINL,Ps in more general settings.In order to solve MINLPs at scales beyond what is currently possible, we consider the study and improvem,ent of the branch-and-bound (BnB) paradigm. In particular, the key optimization techniques that we plan to explore are: (i) Improvin,g (and also appropriate selection of) structure aware large-scale first order methods (FOMs) to solve convex relaxations at each nod,e within a BnB framework. Such an integration of FOM and BnB into a coherent framework could eventually help to solve MINLPs at scal,es much larger than what is currently possible. (ii) Explore the effect of different formulations for MINLPs. This topic is better u,nderstood in the case of MILPs, however not much work has been done in the case of MINLPs. (iii) Design techniques to exploit the u,nderlying statistical assumptions of data for the MINLPs arising from statistical learning applications (iv) Evaluate various critic,al supporting components and methodologies (such as heuristics, branching rules, gradient screening methods, etc.) of a BnB framewor,k, so as to dramatically improve theperformance of the final BnB algorithm.A success in this proposal is poised to lead to new metho,dological advances in algorithms for MINLPs. This will consequently make significant advances in optimization theory and practice, a,nd enrich the statistician?s toolkit for principled computational tools that are currently lacking.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 05, 2022
- Source ID
- N000142212632
Entities
People
- Santanu S. Dey
Organizations
- Georgia Tech Research Corporation
- Office of Naval Research
- United States Navy