Related papers: Automated tight Lyapunov analysis for first-order …
In this paper we prove a Lyapunov type inequality for quasilinear problems with indefinite weights. We show that the first eigenvalue is bounded below in terms of the integral of the weight, instead of the integral of its positive part. We…
This article is a study about the existence and the uniqueness of solutions of a specific quadratic first-order ODE that frequently appears in multiple reconstruction problems. It is called the \emph{planar-perspective equation} due to the…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
The general theory of Lyapunov's stability of first-order differential inclusions in Hilbert spaces has been studied by the authors in a previous work. This new contribution focuses on the natural case when the maximally monotone operator…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and…
In this paper, we reinterpret quadratic Lyapunov functions as solutions to a performance estimation saddle point problem. This allows us to automatically detect the existence of such a Lyapunov function and thus numerically check that a…
We describe an approach for finding upper bounds on an ODE dynamical system's maximal Lyapunov exponent among all trajectories in a specified set. A minimization problem is formulated whose infimum is equal to the maximal Lyapunov exponent,…
We introduce a primal-dual framework for solving linearly constrained nonconvex composite optimization problems. Our approach is based on a newly developed Lagrangian, which incorporates \emph{false penalty} and dual smoothing terms. This…
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…
In this paper, we consider two formulations for Linear Matrix Inequalities (LMIs) under Slater type constraint qualification assumption, namely, SDP smooth and non-smooth formulations. We also propose two first-order linearly convergent…
We present a unified study of first and second order necessary and sufficient optimality conditions for minimax and Chebyshev optimisation problems with cone constraints. First order optimality conditions for such problems can be formulated…
We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…
We focus on nonconvex and nonsmooth minimization problems with a composite objective, where the differentiable part of the objective is freed from the usual and restrictive global Lipschitz gradient continuity assumption. This longstanding…
This paper presents new first-order methods for achieving optimal oracle complexities in convex optimization with convex functional constraints. Oracle complexities are measured by the number of function and gradient evaluations. To achieve…
The goal in this paper is to develop first-order methods equipped with convergence rates for multi-agent optimization problems on semidefinite matrix spaces. These problems include cooperative optimization problems and non-cooperative Nash…
We formulate two classes of first-order algorithms more general than previously studied for minimizing smooth and strongly convex or, respectively, smooth and convex functions. We establish sufficient conditions, via new discrete Lyapunov…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence…
Despite its important applications in Machine Learning, min-max optimization of nonconvex-nonconcave objectives remains elusive. Not only are there no known first-order methods converging even to approximate local min-max points, but the…