Related papers: First-Order Geometry, Spectral Compression, and St…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
In this paper, we propose a descent method for composite optimization problems with linear operators. Specifically, we first design a structure-exploiting preconditioner tailored to the linear operator so that the resulting preconditioned…
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structured problems, these global constants can…
In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…
We consider optimization problems with manifold-valued constraints. These generalize classical equality and inequality constraints to a setting in which both the domain and the codomain of the constraint mapping are smooth manifolds. We…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…
Performance of optimization on quadratic problems sensitively depends on the low-lying part of the spectrum. For large (effectively infinite-dimensional) problems, this part of the spectrum can often be naturally represented or approximated…
We present two first-order, sequential optimization algorithms to solve constrained optimization problems. We consider a black-box setting with a priori unknown, non-convex objective and constraint functions that have Lipschitz continuous…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…
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…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
This paper optimizes the step coefficients of first-order methods for smooth convex minimization in terms of the worst-case convergence bound (i.e., efficiency) of the decrease in the gradient norm. This work is based on the performance…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
This study demonstrates how the adjoint-based framework traditionally used to compute gradients in PDE optimization problems can be extended to handle general constraints on the state variables. This is accomplished by constructing a…
In this paper we consider stochastic composite convex optimization problems with the objective function satisfying a stochastic bounded gradient condition, with or without a quadratic functional growth property. These models include the…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…