Implicit filtering and optimal design problems. (English) Zbl 0821.73040

Gilmore, P.; Kelley, C. T.; Miller, C. T.; Williams, G. A.

Borggaard, Jeffrey (ed.) et al., Optimal design and control. Proceedings of the workshop on optimal design and control, Blacksburg, VA, USA, April 8-9, 1994. Boston, MA: Birkhäuser. Prog. Syst. Control Theory. 19, 159-176 (1995).

Summary: Implicit filtering is a form of the gradient projection method of D. P. Bertsekas [IEEE Trans. automatic Control AC-21, 174-183 (1976; Zbl 0326.49025)] in which the stepsize in a difference approximation of the gradient is changed as the iteration progresses. In this way the algorithm is able to avoid certain types of local minima and in some cases find accurate approximations to the global minimum. The algorithm is particularly effective in avoiding local minima that are caused by high-frequency low-amplitude terms in the objective function. In this report we will discuss the algorithm and its theoretical properties. We will also present applications to modeling of subsurface contaminant transport and high-field magnet design.
For the entire collection see [Zbl 0813.00015].

MSC:

74P99	Optimization problems in solid mechanics
74F15	Electromagnetic effects in solid mechanics
82D40	Statistical mechanical studies of magnetic materials

Keywords:

gradient projection method; iteration progresses; local minima; global minimum; high-frequency low-amplitude terms; subsurface contaminant transport; high-field magnet design

Software:

LANCELOT