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To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....

Convergence of optimal solutions in control problems for hyperbolic equations

S. Migórski (1995)

Annales Polonici Mathematici

A sequence of optimal control problems for systems governed by linear hyperbolic equations with the nonhomogeneous Neumann boundary conditions is considered. The integral cost functionals and the differential operators in the equations depend on the parameter k. We deal with the limit behaviour, as k → ∞, of the sequence of optimal solutions using the notions of G- and Γ-convergences. The conditions under which this sequence converges to an optimal solution for the limit problem are given.

Convergence of primal-dual solutions for the nonconvex log-barrier method without LICQ

Christian Grossmann, Diethard Klatte, Bernd Kummer (2004)

Kybernetika

This paper characterizes completely the behavior of the logarithmic barrier method under a standard second order condition, strict (multivalued) complementarity and MFCQ at a local minimizer. We present direct proofs, based on certain key estimates and few well–known facts on linear and parametric programming, in order to verify existence and Lipschitzian convergence of local primal-dual solutions without applying additionally technical tools arising from Newton–techniques.

Convergence of the Lagrange-Newton method for optimal control problems

Kazimierz Malanowski (2004)

International Journal of Applied Mathematics and Computer Science

Convergence results for two Lagrange-Newton-type methods of solving optimal control problems are presented. It is shown how the methods can be applied to a class of optimal control problems for nonlinear ODEs, subject to mixed control-state constraints. The first method reduces to an SQP algorithm. It does not require any information on the structure of the optimal solution. The other one is the shooting method, where information on the structure of the optimal solution is exploited. In each case,...

Convergence rate of the solutions of singularly perturbed time-optimal control problems

V. M. Veliov (1985)

Banach Center Publications

Crack detection by the topological gradient method

Samuel Amstutz, Imene Horchani, Mohamed Masmoudi (2005)

Control and Cybernetics

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