7,278 research outputs found
Shape optimisation for a class of semilinear variational inequalities with applications to damage models
The present contribution investigates shape optimisation problems for a class
of semilinear elliptic variational inequalities with Neumann boundary
conditions. Sensitivity estimates and material derivatives are firstly derived
in an abstract operator setting where the operators are defined on polyhedral
subsets of reflexive Banach spaces. The results are then refined for
variational inequalities arising from minimisation problems for certain convex
energy functionals considered over upper obstacle sets in . One
particularity is that we allow for dynamic obstacle functions which may arise
from another optimisation problems. We prove a strong convergence property for
the material derivative and establish state-shape derivatives under regularity
assumptions. Finally, as a concrete application from continuum mechanics, we
show how the dynamic obstacle case can be used to treat shape optimisation
problems for time-discretised brittle damage models for elastic solids. We
derive a necessary optimality system for optimal shapes whose state variables
approximate desired damage patterns and/or displacement fields
Sample-path solutions for simulation optimization problems and stochastic variational inequalities
inequality;simulation;optimization
A Coevolutionary Particle Swarm Algorithm for Bi-Level Variational Inequalities: Applications to Competition in Highway Transportation Networks
A climate of increasing deregulation in traditional highway transportation,
where the private sector has an expanded role in the provision of traditional
transportation services, provides a background for practical policy issues to be investigated.
One of the key issues of interest, and the focus of this chapter, would
be the equilibrium decision variables offered by participants in this market. By assuming
that the private sector participants play a Nash game, the above problem can
be described as a Bi-Level Variational Inequality (BLVI). Our problem differs from
the classical Cournot-Nash game because each and every player’s actions is constrained
by another variational inequality describing the equilibrium route choice of
users on the network. In this chapter, we discuss this BLVI and suggest a heuristic
coevolutionary particle swarm algorithm for its resolution. Our proposed algorithm
is subsequently tested on example problems drawn from the literature. The numerical
experiments suggest that the proposed algorithm is a viable solution method for
this problem
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