相关论文: Steepest Descent Algorithm for M-convex Function M…

Finding a local minimum or maximum of a function is often achieved through the gradient-descent optimization method. For a function in dimension d, the gradient requires to compute at each step d partial derivatives. This method is for…

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…

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…

The aim of this paper is to present an original approach that takes advantage from the geometric features of strictly convex functions to tackle the problem of finding the minimum from another perspective. The general idea is that near the…

In this paper we consider a new problem of minimizing an M-convex function under L1-distance constraint (MML1); the constraint is given by an upper bound for L1-distance between a feasible solution and a given "center." This is motivated by…

In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…

This work provides the first convergence analysis for the Randomized Block Coordinate Descent method for minimizing a function that is both H\"older smooth and block H\"older smooth. Our analysis applies to objective functions that are…

The gradient method for minimize a differentiable convex function on Riemannian manifolds with lower bounded sectional curvature is analyzed in this paper. The analysis of the method is presented with three different finite procedures for…

The breakthrough ideas in the modern proximal splitting methodologies allow us to express the set of all minimizers of a superposition of multiple nonsmooth convex functions as the fixed point set of computable nonexpansive operators. In…

This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function F , defined as the expectation of a non convex, non smooth, locally Lipschitz random function. As the…

Stochastic gradient descent type methods are ubiquitous in machine learning, but they are only applicable to the optimization of differentiable functions. Proximal algorithms are more general and applicable to nonsmooth functions. We…

We propose an efficient distributed randomized coordinate descent method for minimizing regularized non-strongly convex loss functions. The method attains the optimal $O(1/k^2)$ convergence rate, where $k$ is the iteration counter. The core…

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…

We propose a new stochastic coordinate descent method for minimizing the sum of convex functions each of which depends on a small number of coordinates only. Our method (APPROX) is simultaneously Accelerated, Parallel and PROXimal; this is…

A number of variable selection methods have been proposed involving nonconvex penalty functions. These methods, which include the smoothly clipped absolute deviation (SCAD) penalty and the minimax concave penalty (MCP), have been…

The purpose of this paper is to propose and analyze a multi-step iterative algorithm to solve a convex optimization problem and a fixed point problem posed on a Hadamard space. The convergence properties of the proposed algorithm are…

We focus on solving constrained convex optimization problems using mini-batch stochastic gradient descent. Dynamic sample size rules are presented which ensure a descent direction with high probability. Empirical results from two…

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

Robot footstep planning strategies can be divided in two main approaches: discrete searches and continuous optimizations. While discrete searches have been broadly applied, continuous optimizations approaches have been restricted for…