Prashant Palkar – Optimization Online

Linearization and Parallelization Schemes for Convex Mixed-Integer Nonlinear Optimization

Published: 2020/05/14, Updated: 2022/02/03

(Mixed) Integer Nonlinear Programming, Parallel Algorithms Branch-and-Bound, convex minlp, linearization techniques, outer approximation, shared-memory parallel

We develop and test linearization and parallelization schemes for convex mixed-integer nonlinear programming. Several linearization approaches are proposed for LP/NLP based branch-and-bound. Some of these approaches strengthen the linear approximation to nonlinear constraints at the root node and some at the other branch-and-bound nodes. Two of the techniques are specifically applicable to commonly found univariate … Read more

A Method for Convex Black-Box Integer Global Optimization

Published: 2019/03/26

Convex Optimization derivative-free optimization, global optimization, integer programming, simulation-based optimization

We study the problem of minimizing a convex function on the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective but, rather, uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings … Read more