Convex integer optimization with Frank-Wolfe methods [article]

Deborah Hendrych and Hannah Troppens and Mathieu Besançon and Sebastian Pokutta
2022 arXiv   pre-print
Mixed-integer nonlinear optimization is a broad class of problems that feature combinatorial structures and nonlinearities. Typical exact methods combine a branch-and-bound scheme with relaxation and separation subroutines. We investigate the properties and advantages of error-adaptive first-order methods based on the Frank-Wolfe algorithm for this setting, requiring only a gradient oracle for the objective function and linear optimization over the feasible set. In particular, we will study the
more » ... algorithmic consequences of optimizing with a branch-and-bound approach where the subproblem is solved over the convex hull of the mixed-integer feasible set thanks to linear oracle calls, compared to solving the subproblems over the continuous relaxation of the same set. This novel approach computes feasible solutions while working on a single representation of the polyhedral constraints, leveraging the full extent of Mixed-Integer Programming (MIP) solvers without an outer approximation scheme.
arXiv:2208.11010v4 fatcat:xne4wzi5jjfqhfwpho7f6seyz4