Related papers: Constructing lattice-free gradient polyhedra in di…

We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and…

In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…

We develop an algorithm that combines model-based and model-free methods for solving a nonlinear optimal control problem with a quadratic cost in which the system model is given by a linear state-space model with a small additive nonlinear…

This paper presents a method to compute differentiable collision-free parametric corridors. In contrast to existing solutions that decompose the obstacle-free space into multiple convex sets, the continuous corridors computed by our method…

The training of machine learning models is typically carried out using some form of gradient descent, often with great success. However, non-asymptotic analyses of first-order optimization algorithms typically employ a gradient smoothness…

We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…

We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-{\L}ojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive…

Using double-smoothing technique and stochastic mirror descent with inexact oracle we built an optimal algorithm (up to a multiplicative factor) for two-points gradient-free non-smooth stochastic convex programming. We investigate how much…

In this paper, we propose a random gradient-free method for optimization in infinite dimensional Hilbert spaces, applicable to functional optimization in diverse settings. Though such problems are often solved through finite-dimensional…

We present an improved algorithm for {\em quasi-properly} learning convex polyhedra in the realizable PAC setting from data with a margin. Our learning algorithm constructs a consistent polyhedron as an intersection of about $t \log t$…

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradients. Focusing on non-asymptotic bounds on convergence rates, we show that if pairs of…

Current differentiable renderers provide light transport gradients with respect to arbitrary scene parameters. However, the mere existence of these gradients does not guarantee useful update steps in an optimization. Instead, inverse…

This paper presents a methodology to construct a divergence-free polynomial basis of an arbitrary degree in a simplex (triangles in 2D and tetrahedra in 3D) of arbitrary dimension. It allows for fast computation of all numerical solutions…

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side).…

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational…

This paper investigates whether sequence models can learn to perform numerical algorithms, e.g. gradient descent, on the fundamental problem of least squares. Our goal is to inherit two properties of standard algorithms from numerical…

Consider convex optimization problems subject to a large number of constraints. We focus on stochastic problems in which the objective takes the form of expected values and the feasible set is the intersection of a large number of convex…

An important method to optimize a function on standard simplex is the active set algorithm, which requires the gradient of the function to be projected onto a hyperplane, with sign constraints on the variables that lie in the boundary of…