Related papers: Accuracy Certificates for Convex Minimization with…
While neural networks have achieved high accuracy on standard image classification benchmarks, their accuracy drops to nearly zero in the presence of small adversarial perturbations to test inputs. Defenses based on regularization and…
In this paper we study a nonconvex-strongly-concave constrained minimax problem. Specifically, we propose a first-order augmented Lagrangian method for solving it, whose subproblems are nonconvex-strongly-concave unconstrained minimax…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
First-order methods have been popularly used for solving large-scale problems. However, many existing works only consider unconstrained problems or those with simple constraint. In this paper, we develop two first-order methods for…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…
Motivated by applications in machine learning and operations research, we study regret minimization with stochastic first-order oracle feedback in online constrained, and possibly non-smooth, non-convex problems. In this setting, the…
Recent advances in cutting-plane strategies applied to robust optimization problems show that they are competitive with respect to problem reformulations and interior-point algorithms. However, although its application with polyhedral…
We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…
We present a novel technique for online safety verification of autonomous systems, which performs reachability analysis efficiently for both bounded and unbounded horizons by employing neural barrier certificates. Our approach uses barrier…
Methods to certify the robustness of neural networks in the presence of input uncertainty are vital in safety-critical settings. Most certification methods in the literature are designed for adversarial or worst-case inputs, but researchers…
This thesis focuses on developing and analyzing accelerated and inexact first-order methods for solving or finding stationary points of various nonconvex composite optimization (NCO) problems. The main tools mainly come from variational and…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…
In a recent paper an Inexact Restoration method for solving continuous constrained optimization problems was analyzed from the point of view of worst-case functional complexity and convergence. On the other hand, the Inexact Restoration…
We propose a new first-order augmented Lagrangian algorithm ALCC for solving convex conic programs of the form min{rho(x)+gamma(x): Ax-b in K, x in chi}, where rho and gamma are closed convex functions, and gamma has a Lipschitz continuous…
In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The…
This paper studies how to certify the convergence of Lasserre's hierarchy of semidefinite programming relaxations for solving multivariate polynomial optimization. We propose flat truncation as a general certificate for this purpose. Assume…
In this note we consider spectral cut-off estimators to solve a statistical linear inverse problem under arbitrary white noise. The truncation level is determined with a recently introduced adaptive method based on the classical discrepancy…
Carrying Code (ACC) has recently been proposed as a framework for mobile code safety in which the code supplier provides a program together with an abstraction (or abstract model of the program) whose validity entails compliance with a…
Satisfiability Modulo Theory (SMT) solvers and equality saturation engines must generate proof certificates from e-graph-based congruence closure procedures to enable verification and conflict clause generation. Smaller proof certificates…
In today's AI-assisted software engineering landscape, developers increasingly depend on LLMs that are highly capable, yet inherently imperfect. The tendency of these models to produce incorrect outputs can reduce developer productivity. To…