Extended Formulations for Advanced Mixed Integer Convex Optimization
Abstract
Mixed integer convex optimization (MICONV) combines the use of integer variables and convex constraints to model a wide range of problems in electronics, chemical engineering, sustainability, design, logistics, finance, and defense. It is the natural extension of both convex optimization and mixed integer linear programming (MILP). While both convex optimization and MILP often be solved effectively in practice, MICONV methods and solvers are significantly less developed. This project partially funded several theoretical, algorithmic, and computational developments to further increase the solvability of MICONV problems. The first project accomplishment was to characterize what classes of optimization problems can be modeled as MICONV problems. The second accomplishment was the development of the Pajarito.jl solver for a sub-class of MICONV problems known as mixed integer conic optimization problems (MICONIC). Pajarito.jl is an open-source solver written in the Julia programming language and its key characteristic is the use of conic duality to build polyhedral approximations for the nonlinear constraint in the MICONV problem. The third accomplishment was the development of the Hypatia.jl primal-dual interior point solver for conic optimization problems. Hypatia.jl is also an open-source solver written in the Julia programming language and its key characteristic is its ability to accept a larger set of cone-classes than standard solvers.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 28, 2022
- Accession Number
- AD1165677
Entities
People
- Juan P. Vielma
Organizations
- Massachusetts Institute of Technology