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We apply four different methods to study an intrinsically bang-bang optimal control problem. We study first a relaxed problem that we solve with a naive nonlinear programming approach. Since these preliminary results reveal singular arcs, we then use Pontryagin’s Minimum Principle and apply multiple indirect shooting methods combined with homotopy approach to obtain an accurate solution of the relaxed problem. Finally, in order to recover a purely bang-bang solution for the original problem, we...
The contribution deals with the description of two nonsmooth equation methods for inequality constrained mathematical programming problems. Three algorithms are presented and their efficiency is demonstrated by numerical experiments.
Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed...
This paper investigates bipolar max-min equations which can be viewed as a generalization of fuzzy relational equations with max-min composition. The relation between the consistency of bipolar max-min equations and the classical boolean satisfiability problem is revealed. Consequently, it is shown that the problem of determining whether a system of bipolar max-min equations is consistent or not is NP-complete. Moreover, a consistent system of bipolar max-min equations, as well as its solution set,...
In this paper we present some applications of the J.-L. Lions’ optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control
In this paper we present some applications of the J.-L. Lions' optimal control theory to real life
problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization
of canned foods, optimal management of waste-water treatment plants and noise control
* This work was supported by National Science Foundation grant DMS 9404431.In this paper we prove that the Newton method applied to the
generalized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued map
F acting in Banach spaces, is locally convergent uniformly in the parameter y if
and only if the map (f +F)^(−1) is Aubin continuous at the reference point. We also
show that the Aubin continuity actually implies uniform Q-quadratic convergence
provided that the derivative of f is Lipschitz...
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