Related papers: High dimensional optimization under non-convex exc…
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…
In this paper, we investigate how structural properties of the constraint system impact the oracle complexity of smooth non-convex optimization problems with convex inequality constraints over a simple polytope. In particular, we show that,…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
We employ the principle of minimum pressure gradient to transform problems in unsteady computational fluid dynamics (CFD) into a convex optimization framework subject to linear constraints. This formulation permits solving, for the first…
This paper considers structural optimization under a reliability constraint, where the input distribution is only partially known. Specifically, when we only know that the expected value vector and the variance-covariance matrix of the…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
This manuscript develops a new framework to analyze and design iterative optimization algorithms built on the notion of Integral Quadratic Constraints (IQC) from robust control theory. IQCs provide sufficient conditions for the stability of…
Our focus is on simulating the dynamics of non-interacting particles including the effects of an external potential, which, under certain assumptions, can be formally described by the Dean-Kawasaki equation. The Dean-Kawasaki equation can…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
We study a nonsmooth nonconvex optimization problem defined over nonconvex constraints, where the feasible set is given by the intersection of the closure of an open set and a smooth manifold. By endowing the open set with a Riemannian…
Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly…
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact…
We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
In a Hilbert space $H$, in order to develop fast optimization methods, we analyze the asymptotic behavior, as time $t$ tends to infinity, of inertial continuous dynamics where the damping acts as a closed-loop control. The function $f: H…
For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set…
We consider the problem of chasing convex functions, where functions arrive over time. The player takes actions after seeing the function, and the goal is to achieve a small function cost for these actions, as well as a small cost for…