## Contributed Session Tue.1.H 2036

#### Tuesday, 10:30 - 12:00 h, Room: H 2036

**Cluster 4: Conic programming** [...]

### Smoothing methods for symmetric cone complementarity problems

**Chair: Shunsuke Hayashi**

**Tuesday, 10:30 - 10:55 h, Room: H 2036, Talk 1**

**Cong Cheng**

A smoothing method for symmetric cone complementarity problems

**Coauthor: Lixin Tang**

**Abstract:**

This paper considers the mathematical program with symmetric cone complementarity constraints (MPSCCC), which is a general form for the nonlinear complementarity problem (NLP), the semi-definite complementarity problem (SDCP), and the second-order complementarity problem (SOCP). The necessary optimality condition and the second order sufficient condition are proposed. By means of the smoothed Fischer-Burmeister function, the smoothing Newton method is employed to solve the problem. At last, a inverse problem which actually is a NLP, is solved as an example.

**Tuesday, 11:00 - 11:25 h, Room: H 2036, Talk 2**

**Ellen Hidemi Fukuda**

Differentiable exact penalty functions for nonlinear second-order cone programs

**Coauthors: Masao Fukushima, Paulo J. S. Silva**

**Abstract:**

We propose a method to solve nonlinear second-order cone programs (SOCPs), that uses a continuously differentiable exact penalty function as a base. The construction of the penalty function is given by incorporating a multipliers estimate in the augmented Lagrangian for SOCPs. Under the nondegeneracy assumption and the strong second-order sufficient condition, we show that a generalized Newton method has global and superlinear convergence. We also present some preliminary numerical experiments.

**Tuesday, 11:30 - 11:55 h, Room: H 2036, Talk 3**

**Shunsuke Hayashi**

A smoothing SQP method for mathematical programs with second-order cone complementarity constraints

**Coauthors: Masao Fukushima, Takayuki Okuno, Hiroshi Yamamura**

**Abstract:**

We focus on the mathematical program with second-order cone complementarity constraints, which contains the well-known mathematical program with nonnegative complementarity constraints as a subclass. For solving such a problem, we propose an algorithm based on the smoothing and the sequential quadratic programming (SQP) methods. We first replace the second-order cone complementarity constraints with equality constraints using the smoothing natural residual function, and apply the SQP method to the smoothed problem while decreasing the smoothing parameter. The SQP type method proposed in this paper has an advantage that the exact solution of each subproblem can be calculated easily since it is a convex quadratic programming problem. We further show that the proposed algorithm possesses the global convergence property under the Cartesian *P*_{0} and some nonsingularity assumptions. We also observe the effectiveness of the algorithm by means of numerical experiments.