Related papers: Lyapunov Functions for First-Order Methods: Tight …

In this paper, we propose two novel non-stationary first-order primal-dual algorithms to solve nonsmooth composite convex optimization problems. Unlike existing primal-dual schemes where the parameters are often fixed, our methods use…

Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To…

This paper is concerned with the problem of finding a quadratic common Lyapunov function for a family of stable linear systems. We present gradient iteration algorithms which give deterministic convergence for finite system families and…

This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…

First-order methods underpin most large-scale learning algorithms, yet their classical convergence guarantees hinge on carefully scheduled step-sizes that depend on the total horizon $T$, which is rarely known in advance. The Schedule-Free…

This paper proposes novel approaches for designing control Lyapunov functions (CLFs) for constrained linear systems. We leverage recent configuration-constrained polyhedral computing techniques to devise piecewise affine convex CLFs.…

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…

We propose a sampling-based approach to learn Lyapunov functions for a class of discrete-time autonomous hybrid systems that admit a mixed-integer representation. Such systems include autonomous piecewise affine systems, closed-loop…

We study the problem of synthesizing polyhedral Lyapunov functions for hybrid linear systems. Such functions are defined as convex piecewise linear functions, with a finite number of pieces. We first prove that deciding whether there exists…

This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains…

This paper presents an efficient, offline method to simultaneously synthesize controllers and seek closed-loop Lyapunov functions for constrained piecewise affine systems on triangulated subsets of the admissible states. Triangulation…

In this work, we present a novel algorithm design methodology that finds the optimal algorithm as a function of inequalities. Specifically, we restrict convergence analyses of algorithms to use a prespecified subset of inequalities, rather…

A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as…

We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…

We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…

What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal…

This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial…

In this paper, we address the problem of discovering maximal Lyapunov functions, as a means of determining the region of attraction of a dynamical system. To this end, we design a novel neural network architecture, which we prove to be a…

The standard assumption for proving linear convergence of first order methods for smooth convex optimization is the strong convexity of the objective function, an assumption which does not hold for many practical applications. In this…

Motivated by applications to distributed optimization over networks and large-scale data processing in machine learning, we analyze the deterministic incremental aggregated gradient method for minimizing a finite sum of smooth functions…