Abstract
In this paper we study the welldefinedness of the central path associated to a nonlinear convex semidefinite programming problem with smooth objective and constraint functions. Under standard assumptions, we prove that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point. The monotonic behavior of the primal and dual logarithmic barriers and of the primal and dual objective functions along the trajectory is also discussed. The existence and optimality of cluster points is established and finally, under the additional assumption of analyticity of the data functions, the convergence of the primal-dual trajectory is proved.
Original language | English |
---|---|
Pages (from-to) | 207-233 |
Number of pages | 27 |
Journal | Optimization |
Volume | 51 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2002 |
Externally published | Yes |
Bibliographical note
Funding Information:*Corresponding author. The work of this author was supported by a post-doctoral fellowship within the Department of Mathematics of the University of Haifa. e-mail: Im [email protected] c-mail: [email protected] ISSN: 0233-1934. Online ISSN: 1029-4945. 0 2002 Taylor & Francis Ltd DOI: lO.lO8O/O233l93O29OOl9396
Keywords
- Central path
- Convex programming
- Logarithmic barrier function
- Nonlinear semidefinite programming
- O-minimal structures
- Semidefinite programming
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics