Operations Research Transactions ›› 2012, Vol. 16 ›› Issue (4): 112-124.

• Original Articles • Previous Articles    

Some results of convex programming complexity

LOU Ye1,2  GAO Yuetian1   

  1. 1. Department of Mathematics, Shanghai University 2. Shanghai Vocational College of Science and Technology
  • Online:2012-12-15 Published:2012-12-15
  • Contact: LOU Ye

Abstract: Recently a number of papers were written that present low-complexity interior-point methods for different classes of convex programs. To guarantee the polynomiality of the procedure, in this paper we show that the logarithmic barrier function associated with these programs is self-concordant. In other words, we will present two different lemmas with different logarithmic barrier functions and apply them to several classes of structured convex optimization problems, using the self-concordancy.

Key words: convex programming, self-concordant barrier functions, entropy programming, optimization complexity

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