The central path in smooth convex semidefinite programs

L. M. Graña Drummond, Y. Peterzil

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)207-233
Number of pages27
Issue number2
StatePublished - Apr 2002
Externally publishedYes

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


  • 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


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