Tuesday, 15:45 - 16:10 h, Room: H 0107

 

Atsushi Kato
An interior point method with a primal-dual quadratic barrier penalty function for nonlinear semidefinite programming

Coauthors: Hiroshi Yabe, Hiroshi Yamashita

 

Abstract:
In this talk, we consider a primal-dual interior point method for nonlinear semidefinite programming problem:
\begin{eqnarray}
{
\begin{array}{lll}
min  & f(x), &  x ∈ {\bf R}n, \ 
s.t.  & g(x)=0, &  X(x) \succeq 0,
\end{array}
.
\nonumber
\end{eqnarray}
where functions f:{\bf R}n → {\bf R}, g:{\bf R}n → {\bf R}m and X:{\bf R}n → {\bf S}p
are sufficiently smooth, and {\bf S}p denotes the set of p-th order real symmetric matrices.
\par
Our method is consists of the outer iteration (SDPIP) and the inner iteration (SDPLS).
Algorithm SDPIP finds a KKT point.
Algorithm SDPLS also finds an approximate shifted barrier KKT point. Specifically, we apply the Newton method to the shifted barrier KKT conditions. To globarize the method, we propose a differentiable merit function in the primal-dual space within the framework of line search strategy. We show its global convergence property.

 

Talk 2 of the contributed session Tue.3.H 0107
"Interior-point methods" [...]
Cluster 16
"Nonlinear programming" [...]

 

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