相关论文: Note on Steepest Descent Algorithm for Quasi L$^{\…

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…

We study the asymptotic shape of the trajectory of the stochastic gradient descent algorithm applied to a convex objective function. Under mild regularity assumptions, we prove a functional central limit theorem for the properly rescaled…

In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal…

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…

We propose several adaptive algorithmic methods for problems of non-smooth convex optimization. The first of them is based on a special artificial inexactness. Namely, the concept of inexact ($ \delta, \Delta, L$)-model of objective…

In this paper, we study the convergence rate of the gradient (or steepest descent) method with fixed step lengths for finding a stationary point of an $L$-smooth function. We establish a new convergence rate, and show that the bound may be…

We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…

In this paper, we define a new type of nonsmooth convex function, called {\em first-order SDSOS-convex semi-algebraic function}, which is an extension of the previously proposed first-order SDSOS-convex polynomials (Chuong et al. in J…

In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…

We propose a descent subgradient algorithm for minimizing a real function, assumed to be locally Lipschitz, but not necessarily smooth or convex. To find an effective descent direction, the Goldstein subdifferential is approximated through…

Discrete convex functions are used in many areas, including operations research, discrete-event systems, game theory, and economics. The objective of this paper is to offer a survey on fundamental operations for various kinds of discrete…

A generalized conditional gradient method for minimizing the sum of two convex functions, one of them differentiable, is presented. This iterative method relies on two main ingredients: First, the minimization of a partially linearized…

This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…

We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…

Quasar convexity is a condition that allows some first-order methods to efficiently minimize a function even when the optimization landscape is non-convex. Previous works develop near-optimal accelerated algorithms for minimizing this class…

In this work, we study the iteration complexity of gradient methods for minimizing convex quadratic functions regularized by powers of Euclidean norms. We show that, due to the uniform convexity of the objective, gradient methods have…

We consider a class of multivariate recurrences frequently arising in the worst case analysis of Davis-Putnam-style exponential time backtracking algorithms for NP-hard problems. We describe a technique for proving asymptotic upper bounds…

We consider the problem of minimizing a strongly convex function that depends on an uncertain parameter $\theta$. The uncertainty in the objective function means that the optimum, $x^*(\theta)$, is also a function of $\theta$. We propose an…

The graduated optimization approach is a method for finding global optimal solutions for nonconvex functions by using a function smoothing operation with stochastic noise. This paper makes three contributions regarding graduated…

Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…