Dislocation hyperbolic augmented Lagrangian algorithm in convex programming

被引：2

作者：

Ramirez, Lennin Mallma ^{[1
]}

Maculan, Nelson ^{[2
]}

Xavier, Adilson Elias ^{[1
]}

Xavier, Vinicius Layter ^{[3
]}

机构：

[1] Univ Fed Rio de Janeiro, Syst Engn & Comp Sci Program COPPE, Rio De Janeiro, Brazil

[2] Univ Fed Rio de Janeiro, Syst Engn & Comp Sci Program Appl Math IM COPPE, Rio De Janeiro, Brazil

[3] Univ Estado Rio De Janeiro, Inst Math & Stat, Grad Program Computat Sci, Rio De Janeiro, Brazil

来源：

INTERNATIONAL JOURNAL OF OPTIMIZATION AND CONTROL-THEORIES & APPLICATIONS-IJOCTA | 2024年 / 14卷 / 02期

关键词：

Augmented Lagrangian; Constrained optimization; Convergence; Convex problem;

D O I：

10.11121/ijocta.1402

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) is a new approach to the hyperbolic augmented Lagrangian algorithm (HALA). DHALA is designed to solve convex nonlinear programming problems. We guarantee that the sequence generated by DHALA converges towards a KarushKuhn-Tucker point. We are going to observe that DHALA has a slight computational advantage in solving the problems over HALA. Finally, we will computationally illustrate our theoretical results.

引用

页码：147 / 155

页数：9

共 20 条

[1] Interior proximal and multiplier methods based on second order homogeneous kernels [J].

Auslender, A ;

Teboulle, M ;

Ben-Tiba, S .

MATHEMATICS OF OPERATIONS RESEARCH, 1999, 24 (03) :645-668

[2]

Belloufi M., 2013, An International Journal of Optimization and Control: Theories C Applications (IJOCTA), V3, P145, DOI [10.11121/ijocta.01.2013.00141, DOI 10.11121/IJOCTA.01.2013.00141]

[3] Worst-case evaluation complexity of a quadratic penalty method for nonconvex optimization [J].

Grapiglia, Geovani Nunes .

OPTIMIZATION METHODS & SOFTWARE, 2023, 38 (04) :781-803

[4] ITERATIVE DETERMINATION OF PARAMETERS FOR AN EXACT PENALTY FUNCTION [J].

HARTMAN, JK .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1975, 16 (1-2) :49-66

[5]

Harwell Subroutine Library, 2002, A collection of Fortran codes for large scale scientific computation

[6]

Hock W., 1981, Lecture Notes in Economics and Mathematical Systems, V187, DOI [10.1007/978-3-642-48320-2, DOI 10.1007/978-3-642-48320-2]

[7] An example comparing the standard and safeguarded augmented Lagrangian methods [J].

Kanzow, Christian ;

Steck, Daniel .

OPERATIONS RESEARCH LETTERS, 2017, 45 (06) :598-603

[8] COMBINED PRIMAL-DUAL AND PENALTY METHODS FOR CONVEX PROGRAMMING [J].

KORT, BW ;

BERTSEKAS, DP .

SIAM JOURNAL ON CONTROL, 1976, 14 (02) :268-294

[9]

Mallma-Ramirez Lennin, 2022, Ph. D. Thesis

[10] Nonlinear rescaling and proximal-like methods in convex optimization [J].

Polyak, R ;

Teboulle, M .

MATHEMATICAL PROGRAMMING, 1997, 76 (02) :265-284

← 1 2 →