### Thursday, July 17

3:15 PM-5:15 PM

*Building 200, Room 2*

## MS70

Complementary-Dual Variational Principles and Numerical Methods (Part I of III)

Complementary-dual variational methods play an important role in nonlinear optimization, partial differential equations, control theory, continuum mechanics, optimal design, mechanical systems and economics, game theory, and computational methods. Much research has been devoted to the developments of complementary variational principles in the last forty years. The theory is well developed in several directions, for example in linear/nonlinear optimization and variational problems, solid mechanics, optimal control, and finite element methods, etc., the complementary-dual variational method has made substantial contributions.

The speakers in this minisymposium will present progress made in their respective areas of study with theory and applications in nonsmooth analysis, solid mechanics, differential geometry, optimal control, nonlinear bifurcation analysis and buckling problems, finite element methods, etc.

It is known that in nonlinear/nonsmooth systems, the traditional direct methods or Ritz methods for solving nonconvex variational problems are usually very difficult or even impossible. However, the dual variational principles may provide a potentially useful alternative methods. Apart from providing a more complete picture of variational methods, the complementary formulations often provide useful bounds on some important parameters of interest.

**Organizers: David Y. Gao, Virginia Polytechnic Institute and State University; Bez Tabarrok, University of Victoria, Canada; and R. W. Ogden, University of Glasgow, United Kingdom**

**Chair: Bez Tabarrok, Organizer**

**3:15 Aspects of Complementary Variational Principles in Nonlinear Elasticity**
- R. W. Ogden, Organizer
**3:45 The Torsion Problem in Finite Elasticity Theory with Non-Smooth Internal Strain**
- Konstantinos A. Lazopoulos, National Technical University of Athens, Greece
**4:15 Dual Extremum Principles in the Finite Elastostatics of Tension Structures **
- David Steigmann, University of California, Berkeley
**4:45 Duality Theory in Finite Deformation Unstable Systems with Applications in Phase Transitions and Post-Buckling Analysis**
- David Y. Gao, Organizer

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*TMP, 4/4/97*

*MMD, 5/30/97*