A Monotonicity Result for Norms in Conjugate Gradient Algorithms

被引：0

作者：

Anton Schiela

机构：

[1] Universität Bayreuth,

来源：

Journal of Optimization Theory and Applications | 2023年 / 196卷

关键词：

Conjugate gradients; Quadratic optimization; Monotonicity of norms; 90C06; 65J10; 90C48;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show a monotonicity result, enjoyed by norms of iterates of the cg method. It relates the energy norm and the norm, induced by the preconditioner. We place this result into the context of known results and sketch possible applications to ill-posed problems and in unconstrained optimization. Finally, we give some illustration by a numerical example.

引用

页码：126 / 146

页数：20

共 50 条

[41] REGULARIZING ALGORITHMS BASED ON THE CONJUGATE-GRADIENT METHOD
GILYAZOV, SF
[J]. USSR COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 1986, 26 (01): : 8 - 13
[42] Monotonicity and *orthant-monotonicity of certain maximum norms
Lavric, B
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2003, 367 : 29 - 36
[43] Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds
Xiaojing Zhu
Hiroyuki Sato
[J]. Advances in Computational Mathematics, 2021, 47
[44] Cayley-transform-based gradient and conjugate gradient algorithms on Grassmann manifolds
Zhu, Xiaojing
Sato, Hiroyuki
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2021, 47 (04)
[45] Monotonicity of unitarily invariant norms
Wang, Xue-Feng
Li, Ren-Cang
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 466 : 254 - 266
[46] MONOTONICITY OF LP AND LP NORMS
HWANG, SY
[J]. IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1975, 23 (06): : 593 - 594
[47] RELATIONSHIP BETWEEN THE BFGS AND CONJUGATE GRADIENT ALGORITHMS AND ITS IMPLICATIONS FOR NEW ALGORITHMS
NAZARETH, L
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1979, 16 (05) : 794 - 800
[48] CONJUGATE GRADIENT ALGORITHMS - QUADRATIC TERMINATION WITHOUT LINEAR SEARCHES
DIXON, LCW
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS AND ITS APPLICATIONS, 1975, 15 (01): : 9 - 18
[49] GPU-Based Parallel Nonlinear Conjugate Gradient Algorithms
Galiano, V.
Migallon, H.
Migallon, V.
Penades, J.
[J]. PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING, 2011, 95
[50] Open Problems in Nonlinear Conjugate Gradient Algorithms for Unconstrained Optimization
Andrei, Neculai
[J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2011, 34 (02) : 319 - 330

← 1 2 3 4 5 →