Related papers: Line Search Fixed Point Algorithms Based on Nonlin…
This article presents nonlinear conjugate gradient methods for finding local weakly minimal points of set-valued optimization problems under a lower set less ordering relation. The set-valued objective function of the optimization problem…
This paper addresses unconstrained multiobjective optimization problems where two or more continuously differentiable functions have to be minimized. We delve into the conjugate gradient methods proposed by Lucambio P\'{e}rez and Prudente…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
The problem of minimizing the sum of nonsmooth, convex objective functions defined on a real Hilbert space over the intersection of fixed point sets of nonexpansive mappings, onto which the projections cannot be efficiently computed, is…
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
In this paper, we combine the $m$th-order Taylor expansion of the objective function with cubic Hermite interpolation conditions. Then, we derive a series of modified secant equations with higher accuracy in approximation of the Hessian…
We propose a descent subgradient algorithm for unconstrained nonsmooth nonconvex multiobjective optimization problems. To find a descent direction, we present an iterative process that efficiently approximates the Goldstein subdifferential…
In this article, we propose an algorithm for the nonlinear conjugate gradient method to find a Pareto critical point of unconstrained multiobjective interval optimization problems. In this algorithm, we use the Wolfe line search procedure…
Nonlinear conjugate gradients are among the most popular techniques for solving continuous optimization problems. Although these schemes have long been studied from a global convergence standpoint, their worst-case complexity properties…
The proximal point algorithm is a widely used tool for solving a variety of convex optimization problems such as finding zeros of maximally monotone operators, fixed points of nonexpansive mappings, as well as minimizing convex functions.…
This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…
In deterministic optimization, line searches are a standard tool ensuring stability and efficiency. Where only stochastic gradients are available, no direct equivalent has so far been formulated, because uncertain gradients do not allow for…
We consider a variable metric linesearch based proximal gradient method for the minimization of the sum of a smooth, possibly nonconvex function plus a convex, possibly nonsmooth term. We prove convergence of this iterative algorithm to a…
Line search (or backtracking) procedures have been widely employed into first-order methods for solving convex optimization problems, especially those with unknown problem parameters (e.g., Lipschitz constant). In this paper, we show that…
It has long been known that the gradient (steepest descent) method may fail on nonsmooth problems, but the examples that have appeared in the literature are either devised specifically to defeat a gradient or subgradient method with an…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…