Convergence Analysis of Difference-of-Convex Algorithm with Subanalytic Data

Difference-of-Convex programming and related algorithms, which constitute the backbone of nonconvex programming and global optimization, were introduced in 1985 by Pham Dinh Tao and have been extensively developed by Le Thi Hoai An and Pham Dinh Tao since 1994 to become now classic and increasingly...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of optimization theory and applications Jg. 179; H. 1; S. 103 - 126
Hauptverfasser: Le Thi, Hoai An, Huynh, Van Ngai, Pham Dinh, Tao
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.10.2018
Springer Nature B.V
Springer Verlag
Schlagworte:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computational geometry
Continuity (mathematics)
Convergence
Convexity
Critical point
Engineering
Global optimization
Mathematical programming
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Theory of Computation
Difference-of-Convex algorithm
90C30
Subdifferential
Subanalyticity
Convergence rate
Lojasiewicz exponent
90C26
47N10
Difference-of-Convex programming
ISSN:0022-3239, 1573-2878
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:Difference-of-Convex programming and related algorithms, which constitute the backbone of nonconvex programming and global optimization, were introduced in 1985 by Pham Dinh Tao and have been extensively developed by Le Thi Hoai An and Pham Dinh Tao since 1994 to become now classic and increasingly popular. That algorithm is a descent method without linesearch and every limit point of its generated sequence is a critical point of the related Difference-of-Convex program. Determining its convergence rate is a challenging problem. Its knowledge is crucial from both theoretical and practical points of view. In this work, we treat this problem for the class of Difference-of-Convex programs with subanalytic data by using the nonsmooth form of the Lojasiewicz inequality. We have successfully proved that the whole sequence is convergent, if it is bounded, provided that the objective function is subanalytic continuous on its domain and one of the two Difference-of-Convex components is differentiable with locally Lipschitz derivative. We also established a result on the convergence rate, which depended on the Lojasiewicz exponent of the objective function. Finally, for both classes of trust-region subproblems and nonconvex quadratic programs, we showed that the Lojasiewicz exponent was one half, and thereby, our proposed algorithms applied to these Difference-of-Convex programs were Root-linearly convergent.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1345-y