Search Results - subject:"Gradient method"

A variable smoothing algorithm for solving convex optimization problems

Boţ, Radu; Hendrich, Christopher - In: TOP: An Official Journal of the Spanish Society of … 23 (2015) 1, pp. 124-150

In this article, we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth them to convex and differentiable functions with Lipschitz...

Persistent link: https://www.econbiz.de/10011241032

An adaptive accelerated proximal gradient method and its homotopy continuation for sparse optimization

Lin, Qihang; Xiao, Lin - In: Computational Optimization and Applications 60 (2015) 3, pp. 633-674

<Para ID="Par1">We consider optimization problems with an objective function that is the sum of two convex terms: one is smooth and given by a black-box oracle, and the other is general but with a simple, known structure. We first present an accelerated proximal gradient (APG) method for problems where the...</para>

Persistent link: https://www.econbiz.de/10011241264

On the connection between the conjugate gradient method and quasi-Newton methods on quadratic problems

Forsgren, Anders; Odland, Tove - In: Computational Optimization and Applications 60 (2015) 2, pp. 377-392

It is well known that the conjugate gradient method and a quasi-Newton method, using any well-defined update matrix … update matrix lies in the last two dimensions of the Krylov subspaces defined by the conjugate gradient method and that the … obtained in the conjugate gradient method is derived. In addition, we show that the update matrices from the one …

Persistent link: https://www.econbiz.de/10011241268

A family of three-term conjugate gradient methods with sufficient descent property for unconstrained optimization

Al-Baali, Mehiddin; Narushima, Yasushi; Yabe, Hiroshi - In: Computational Optimization and Applications 60 (2015) 1, pp. 89-110

-term conjugate gradient method which satisfies a sufficient descent condition. We extend this method to two parameters family of …

Persistent link: https://www.econbiz.de/10011151822

A variable smoothing algorithm for solving convex optimization problems

Boţ, Radu Ioan; Hendrich, Christopher - In: Top : transactions in operations research 23 (2015) 1, pp. 124-150

Persistent link: https://www.econbiz.de/10011406959

Notes on a 3-term Conjugacy Recurrence for the Iterative Solution of Symmetric Linear Systems

Fasano, Giovanni - Dipartimento di Matematica Applicata, Università Ca' … - 2008

We consider a 3-term recurrence, namely CG_2step, for the iterative solution of symmetric linear systems. The new algorithm generates conjugate directions and extends some standard theoretical properties of the Conjugate Gradient (CG) method [10]. We prove the finite convergence of CG_2step, and...

Persistent link: https://www.econbiz.de/10005566307

On proximal gradient method for the convex problems regularized with the group reproducing kernel norm

Zhang, Haibin; Wei, Juan; Li, Meixia; Zhou, Jie; Chao, … - In: Journal of Global Optimization 58 (2014) 1, pp. 169-188

approach to solve such problems is by the proximal gradient method. In this paper we derive and study theoretically the …

Persistent link: https://www.econbiz.de/10010845793

Path-following gradient-based decomposition algorithms for separable convex optimization

Dinh, Quoc Tran; Necoara, Ion; Diehl, Moritz - In: Journal of Global Optimization 59 (2014) 1, pp. 59-80

dual variables using a path-following gradient method and allows one to solve the subproblems in parallel. Moreover …

Persistent link: https://www.econbiz.de/10010845803

Efficient algorithms for robust and stable principal component pursuit problems

Aybat, Necdet; Goldfarb, Donald; Ma, Shiqian - In: Computational Optimization and Applications 58 (2014) 1, pp. 1-29

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data ranking. It has been shown that under certain...

Persistent link: https://www.econbiz.de/10010847445

Incremental accelerated gradient methods for SVM classification: study of the constrained approach

Couellan, Nicolas; Jan, Sophie - In: Computational Management Science 11 (2014) 4, pp. 419-444

We investigate constrained first order techniques for training support vector machines (SVM) for online classification tasks. The methods exploit the structure of the SVM training problem and combine ideas of incremental gradient technique, gradient acceleration and successive simple...

Persistent link: https://www.econbiz.de/10010949671