Related papers: On Constraints in First-Order Optimization: A View…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
While first-order stationary points (FOSPs) are the traditional targets of non-convex optimization, they often correspond to undesirable strict saddle points. To circumvent this, attention has shifted towards second-order stationary points…
In this effort we propose a data-driven learning framework for reduced order modeling of fluid dynamics. Designing accurate and efficient reduced order models for nonlinear fluid dynamic problems is challenging for many practical…
We study projection-free optimization for convex objectives that satisfy abs-smoothness, a structural property that captures many non-smooth yet piecewise smooth functions arising, e.g., in modern machine learning models. We develop a…
In this paper, we propose a class of super-schemes for efficiently solving nonlinear unconstrained optimization problems. The proposed approach introduces two novel choices of step-size parameters, leading to efficient descent directions…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
This paper presents a framework to solve constrained optimization problems in an accelerated manner based on High-Order Tuners (HT). Our approach is based on reformulating the original constrained problem as the unconstrained optimization…
We consider in this paper a class of single-ratio fractional minimization problems, in which the numerator part of the objective is the sum of a nonsmooth nonconvex function and a smooth nonconvex function while the denominator part is a…
The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…
We consider minimization of stochastic functionals that are compositions of a (potentially) non-smooth convex function $h$ and smooth function $c$ and, more generally, stochastic weakly-convex functionals. We develop a family of stochastic…
We consider the problem of finding an approximate second-order stationary point of a constrained non-convex optimization problem. We first show that, unlike the gradient descent method for unconstrained optimization, the vanilla projected…
Finding the optimal hyperparameters of a model can be cast as a bilevel optimization problem, typically solved using zero-order techniques. In this work we study first-order methods when the inner optimization problem is convex but…
We show that the optimal complexity of Nesterov's smooth first-order optimization algorithm is preserved when the gradient is only computed up to a small, uniformly bounded error. In applications of this method to semidefinite programs,…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
Arising in semi-parametric statistics, control applications, and as sub-problems in global optimization methods, certain optimization problems can have objective functions requiring numerical integration to evaluate, yet gradient function…
In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…
A framework is developed for applying accelerated methods to general hyperbolic programming, including linear, second-order cone, and semidefinite programming as special cases. The approach replaces a hyperbolic program with a convex…
Finite-difference methods are a class of algorithms designed to solve black-box optimization problems by approximating a gradient of the target function on a set of directions. In black-box optimization, the non-smooth setting is…
This paper is devoted to the study of stochastic optimization problems under the generalized smoothness assumption. By considering the unbiased gradient oracle in Stochastic Gradient Descent, we provide strategies to achieve in bounds the…
Modern large-scale statistical models require to estimate thousands to millions of parameters. This is often accomplished by iterative algorithms such as gradient descent, projected gradient descent or their accelerated versions. What are…