Related papers: First-Order Methods for Nonsmooth Nonconvex Functi…
We propose a single time-scale stochastic subgradient method for constrained optimization of a composition of several nonsmooth and nonconvex functions. The functions are assumed to be locally Lipschitz and differentiable in a generalized…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
An algorithm for unconstrained non-convex optimization is described, which does not evaluate the objective function and in which minimization is carried out, at each iteration, within a randomly selected subspace. It is shown that this…
In this paper some adaptive mirror descent algorithms for problems of minimization convex objective functional with several convex Lipschitz (generally, non-smooth) functional constraints are considered. It is shown that the methods are…
In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…
Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
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…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
First-order algorithms have been popular for solving convex and non-convex optimization problems. A key assumption for the majority of these algorithms is that the gradient of the objective function is globally Lipschitz continuous, but…
This paper proposes a novel first-order algorithm that solves composite nonsmooth and stochastic convex optimization problem with function constraints. Most of the works in the literature provide convergence rate guarantees on the…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
We describe a novel constructive technique for devising efficient first-order methods for a wide range of large-scale convex minimization settings, including smooth, non-smooth, and strongly convex minimization. The technique builds upon a…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
In this work, we develop first-order (Hessian-free) and zero-order (derivative-free) implementations of the Cubically regularized Newton method for solving general non-convex optimization problems. For that, we employ finite difference…
First-order methods (FOMs) have recently been applied and analyzed for solving problems with complicated functional constraints. Existing works show that FOMs for functional constrained problems have lower-order convergence rates than those…
We identify and analyze a fundamental limitation of the classical projected subgradient method in nonsmooth convex optimization: the inevitable failure caused by the absence of valid subgradients at boundary points. We show that, under…
A parametric class of trust-region algorithms for constrained nonconvex optimization is analyzed, where the objective function is never computed. By defining appropriate first-order stationarity criteria, we are able to extend the Adagrad…