**数学与系统科学研究院**

**计算数学所学术报告**

**报告人**：
Prof.Ronald H.W. Hoppe

Universitaet Augsburg, Germany

**报告题目**
Primal-Dual Newton Interior-Point Methods
in Structural Optimization

**Abstract:**
The optimization of the shape and the topology of continuum mechanical structures
by means of a systematic, physically consistent design methodology is referred
to as structural optimization. The design criteria are chosen according to
a goal oriented operational behavior of the structures under consideration and
typically lead to nonlinear objective functionals depending on the state variables
describing the operational mode and the design variables determining the
shape and the topology. The state variables are assumed to satisfy di erential
equations reflecting the underlying physical laws whereas technological aspects
may give rise to further equality and inequality constraints on both the state
and the design variables.

After discretization the resulting nonlinear programming problem is usually
solved by what is called an alternating iteration where the discretized state
equations and the optimization are carried out sequentially. Here, we advocate
the use of recently developed ”all-at-once” approaches featuring the numerical
solution of the state equations as an integral part of the optimization routine.
In particular, we focus on primal-dual Newton interior-point methods. Special
emphasis is given on the e±cient solution of the primal-dual Hessian system
and on convergence monitoring by a hierarchy of two merit functions.
Applications include the structural optimization of microcellular biomorphic
ceramics based on homogenization, the shape optimization of electrorheological
shock absorbers, and the topology optimization of high power electromotors,.

**报告时间**：2004年5月31日 下午4：00

**报告地点**：科技综合楼三层报告厅