Related papers: A Frank-Wolfe-based primal heuristic for quadratic…
We consider the problem of solving LP relaxations of MAP-MRF inference problems, and in particular the method proposed recently in (Swoboda, Kolmogorov 2019; Kolmogorov, Pock 2021). As a key computational subroutine, it uses a variant of…
We propose several variants of the Frank-Wolfe algorithm to minimize a sum of functions. The main proposed algorithm is inspired from the dual averaging scheme of Nesterov adapted for Frank Wolfe in a stochastic setting. A distributed…
This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or…
We consider the problem of minimizing a difference of (smooth) convex functions over a compact convex feasible region $P$, i.e., $\min_{x \in P} f(x) - g(x)$, with smooth $f$ and Lipschitz continuous $g$. This computational study builds…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient…
This work addresses the Robust counterpart of the Shortest Path Problem (RSPP) with a correlated uncertainty set. Since this problem is hard, a heuristic approach, based on Frank-Wolfe's algorithm named Discrete Frank-Wolf (DFW), has…
Optimal transport (OT), which provides a distance between two probability distributions by considering their spatial locations, has been applied to widely diverse applications. Computing an OT problem requires solution of linear programming…
Effectively encoding inequality constraints is a primary obstacle in applying quantum algorithms to financial optimization. A quantum model for Markowitz portfolio optimization is presented that resolves this by embedding slack variables…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
In the first part of this dissertation research, we develop a modular framework that can serve as a recipe for constructing and analyzing iterative algorithms for convex optimization. Specifically, our work casts optimization as iteratively…
The Frank-Wolfe algorithm is a popular method in structurally constrained machine learning applications, due to its fast per-iteration complexity. However, one major limitation of the method is a slow rate of convergence that is difficult…
We consider optimization problems in which the goal is find a $k$-dimensional subspace of $\mathbb{R}^n$, $k<<n$, which minimizes a convex and smooth loss. Such problems generalize the fundamental task of principal component analysis (PCA)…
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints. However, in the stochastic learning setting, it…
In this paper, we consider approximate Frank-Wolfe (FW) algorithms to solve convex optimization problems over graph-structured support sets where the linear minimization oracle (LMO) cannot be efficiently obtained in general. We first…
Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly…
We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by…
This paper investigates projection-free algorithms for stochastic constrained multi-level optimization. In this context, the objective function is a nested composition of several smooth functions, and the decision set is closed and convex.…
We present novel mixed-integer programming (MIP) formulations for optimization over nonconvex piecewise linear functions. We exploit recent advances in the systematic construction of MIP formulations to derive new formulations for…
Projection-free block-coordinate methods avoid high computational cost per iteration and at the same time exploit the particular problem structure of product domains. Frank-Wolfe-like approaches rank among the most popular ones of this…