TL;DR
A new method for finding globally maximal solutions for differentiable non-decreasing continuous submodular functions subject to constraints is proposed and a cutting plane algorithm that finds approximate solutions and bounds using an approximation of the convex hull of the hypograph is developed.
An efficient tree-based implementation is developed, which accelerates POA's core subroutines while storing the outer-approximation compactly and introduces polyblocks, an open-source Python package implementing the proposed algorithms alongside a framework for developing new POA variants.
We investigate the optimization problem of minimizing a nonsmooth function that satisfies a nonsmooth version of the descent lemma over a nonempty and closed but not necessarily convex set. The objective function belongs to the class of upper-$\mathcal{C}^2$ functions, whereas the constraints may promote a sparse or lo...
This work considers a quadratic minmax problem with coupled inner constraints and proposes a method to compute a class of stationary points and shows in particular that the method is polynomial in the special case where the inner feasible set of the authors' constrained minmax problem is independent from outer variable...
We introduce Envelopt, a globally convergent iterative framework for a broad class of structured optimization problems where a smooth objective is augmented by a nonsmooth convex regularizer composed with a smooth mapping, and the variables are subject to general smooth constraints. All smooth functions may be nonconve...
We study mixed-integer quadratic fractional optimization problems with binary and continuous box-constrained variables. The objective is the ratio of two quadratic functions, a structure that arises naturally in portfolio selection, signal processing, and data analytics. We propose an exact algorithm based on Dinkelbac...
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