On Two Algorithms for Nonconvex Nonsmooth Optimization Problems in Structural Mechanics

M. Ap. Tzaferopoulos, E. S. Mistakidis, C. D. Bisbos and P. D. Panagiotopoulos
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M. Ap. Tzaferopoulos: Aristotle University, Institute of Steel Structures, Department of Civil Engineering
E. S. Mistakidis: Aristotle University, Institute of Steel Structures, Department of Civil Engineering
C. D. Bisbos: Aristotle University, Institute of Steel Structures, Department of Civil Engineering
P. D. Panagiotopoulos: Aristotle University, Institute of Steel Structures, Department of Civil Engineering

A chapter in Large Scale Optimization, 1994, pp 428-456 from Springer

Abstract: Abstract The variational formulation of Structural Mechanics problems, when the material and boundary laws are assumed monotone, leads to variational inequalities (symmetric or not), that can be solved using modern convex minimization or nonlinear complementarity methods. In order to describe the gradual loss of strength, nonmonotone and possibly multivalued laws have been introduced recently, that give rise to hemivariational inequalities. Due to the lack of convexity and the nonsmoothness of the underlying (super) potentials those problems have generally nonunique solutions (stable or unstable). In the present paper a pair of methods for the decomposition of hemivariational inequalities to a finite number of variational inequalities is proposed. The first method is based on the decomposition of the contigent cone of the superpotential into convex constituents, while in the second the nonconvex superpotential is approximated locally by convex superpotentials. Both approaches lead to effective, reliable and versatile numerical algorithms for large scale hemivariational inequalities. Concluding, numerical examples illustrate the properties and applicability of the methods.

Keywords: Hemivariational inequalities; nonconvex superpotentials; convex minimization; structural mechanics; nonlinear complementarity (search for similar items in EconPapers)
Date: 1994
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DOI: 10.1007/978-1-4613-3632-7_21

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