Related papers: Nonlinear Conjugate Gradient Method for Multiobjec…
This paper proposes a new steepest gradient descent method for solving nonconvex finite minimax problems using non-monotone adaptive step sizes and providing proof of convergence results in cases of the nonconvex, quasiconvex, and…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…
Shape optimization based on shape calculus has received a lot of attention in recent years, particularly regarding the development, analysis, and modification of efficient optimization algorithms. In this paper we propose and investigate…
This paper explores variants of the subspace iteration algorithm for computing approximate invariant subspaces. The standard subspace iteration approach is revisited and new variants that exploit gradient-type techniques combined with a…
In this paper, we propose a scaled gradient modified non-monotone line search method for solving constrained minimization problems, and explore several specific properties of this method, namely, its convergence analysis. We discuss the…
This article describes a new Riemannian conjugate gradient method and presents a global convergence analysis. The existing Fletcher-Reeves-type Riemannian conjugate gradient method is guaranteed to be globally convergent if it is…
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…
This paper investigates the point convergence of accelerated gradient methods for multiobjective optimization, in both continuous and discrete settings. We address the open problems of whether the solution trajectory of the multiobjective…
Gradient algorithms are classical in adaptive control and parameter estimation. For instantaneous quadratic cost functions they lead to a linear time-varying dynamic system that converges exponentially under persistence of excitation…
In this paper, a tunneling method is developed for nonlinear multiobjective optimization problems using some ideas of the single objective tunneling method. The proposed method does not require any a priori chosen parameters or ordering…
In this paper, we propose a globally convergent method for solving constrained nonlinear systems. The method combines an efficient Newton conditional gradient method with a derivative-free and nonmonotone linesearch strategy. The global…
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…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds at best when applied to smooth convex functions. In contrast, Nesterov's accelerated…
Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…
In this paper, we derive a new linear convergence rate for the gradient method with fixed step lengths for non-convex smooth optimization problems satisfying the Polyak-Lojasiewicz (PL) inequality. We establish that the PL inequality is a…
In this paper, we consider the nonconvex quadratically constrained quadratic programming (QCQP) with one quadratic constraint. By employing the conjugate gradient method, an efficient algorithm is proposed to solve QCQP that exploits the…
We propose a computer-assisted approach to the analysis of the worst-case convergence of nonlinear conjugate gradient methods (NCGMs). Those methods are known for their generally good empirical performances for large-scale optimization,…