Log-Sigmoid nonlinear Lagrange method for nonlinear optimization problems over second-order cones

✍ Scribed by Jian Gu; Liwei Zhang; Xiantao Xiao

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 862 KB
• Volume: 229
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2008.10.016

✦ Synopsis

This paper analyzes the rate of local convergence of the Log-Sigmoid nonlinear Lagrange method for nonconvex nonlinear second-order cone programming. Under the componentwise strict complementarity condition, the constraint nondegeneracy condition and the second-order sufficient condition, we show that the sequence of iteration points generated by the proposed method locally converges to a local solution when the penalty parameter is less than a threshold and the error bound of solution is proportional to the penalty parameter. Finally, we report numerical results to show the efficiency of the method.