Related papers: Optimizing Star-Convex Functions
In this paper we consider a distributed stochastic optimization problem without the gradient/subgradient information for the local objective functions, subject to local convex constraints. The objective functions may be non-smooth and…
In the field of global optimization, many existing algorithms face challenges posed by non-convex target functions and high computational complexity or unavailability of gradient information. These limitations, exacerbated by sensitivity to…
In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
We prove non asymptotic polynomial bounds on the convergence of the Langevin Monte Carlo algorithm in the case where the potential is a convex function which is globally Lipschitz on its domain, typically the maximum of a finite number of…
In this paper, we propose two algorithms for solving convex optimization problems with linear ascending constraints. When the objective function is separable, we propose a dual method which terminates in a finite number of iterations. In…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
When computing bounds, spatial branch-and-bound algorithms often linearly outer approximate convex relaxations for non-convex expressions in order to capitalize on the efficiency and robustness of linear programming solvers. Considering…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
We introduce a notion of inexact model of a convex objective function, which allows for errors both in the function and in its gradient. For this situation, a gradient method with an adaptive adjustment of some parameters of the model is…
We provide a simple and flexible framework for designing differentially private algorithms to find approximate stationary points of non-convex loss functions. Our framework is based on using a private approximate risk minimizer to "warm…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
Recently some specific classes of non-smooth and non-Lipschitz convex optimization problems were selected by Yu.~Nesterov along with H.~Lu. We consider convex programming problems with similar smoothness conditions for the objective…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
This paper addresses the minimization of a finite sum of prox-convex functions under Lipschitz continuity of each component. We propose two variants of the splitting proximal point algorithms proposed in \cite{Bacak,Bertsekas}: one…
This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints…
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…
We propose an accelerated meta-algorithm, which allows to obtain accelerated methods for convex unconstrained minimization in different settings. As an application of the general scheme we propose nearly optimal methods for minimizing…