## Exhibits

 Tuesday, 15:45 - 16:10 h, Room: H 0107  Atsushi KatoAn interior point method with a primal-dual quadratic barrier penalty function for nonlinear semidefinite programmingCoauthors: 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. \parOur 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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