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Displaying 21 –
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399
In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the...
This paper is concerned with the stabilisation of linear time-delay systems by tuning a finite number of parameters. Such problems typically arise in the design of fixed-order controllers. As time-delay systems exhibit an infinite amount of characteristic roots, a full assignment of the spectrum is impossible. However, if the system is stabilisable for the given parameter set, stability can in principle always be achieved through minimising the real part of the rightmost characteristic root, or...
This paper is concerned with the stabilisation of linear time-delay systems
by tuning a finite number of parameters. Such problems typically arise in the
design of fixed-order controllers. As time-delay systems exhibit an infinite amount of
characteristic roots, a full assignment of the spectrum is impossible.
However, if the system is stabilisable for the given parameter set, stability can
in principle always be achieved through minimising the real part of the rightmost
characteristic...
The paper concerns a two-level hierarchical game, where the players on each level behave noncooperatively. In this way one can model eg an oligopolistic market with several large and several small firms. We derive two types of necessary conditions for a solution of this game and discuss briefly the possibilities of its computation.
This note deals with contact shape optimization for problems involving “floating” structures. The boundedness of solutions to state problems with respect to admissible domains, which is the basic step in the existence analysis, is a consequence of Korn’s inequality in coercive cases. In semicoercive cases (meaning that floating bodies are admitted), the Korn inequality cannot be directly applied and one has to proceed in another way: to use a decomposition of kinematically admissible functions and...
The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...
We propose a penalty approach for a box constrained variational inequality problem . This problem is replaced by a sequence of nonlinear equations containing a penalty term. We show that if the penalty parameter tends to infinity, the solution of this sequence converges to that of when the function involved is continuous and strongly monotone and the box contains the origin. We develop the algorithmic aspect with theoretical arguments properly established. The numerical results tested on...
Motivated by the pricing of American options for baskets we
consider a parabolic variational inequality in a bounded
polyhedral domain with a continuous piecewise
smooth obstacle. We formulate a fully discrete method by using
piecewise linear finite elements in space and the backward Euler
method in time. We define an a posteriori error estimator and show
that it gives an upper bound for the error in
L2(0,T;H1(Ω)). The error estimator is localized in the
sense that the size of the elliptic residual...
We examine an elliptic optimal control problem with control and state constraints in ℝ3. An improved error estimate of 𝒪(hs) with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation involving piecewise constant functions for the control and piecewise linear for the state. The derived order of convergence is illustrated by a numerical example.
We examine an elliptic optimal control problem with control and state constraints in
ℝ3. An improved error estimate of
𝒪(hs)
with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation
involving piecewise constant functions for the control and piecewise linear for the state.
The derived order of convergence is illustrated by a numerical example.
We examine an elliptic optimal control problem with control and state constraints in
ℝ3. An improved error estimate of
𝒪(hs)
with 3/4 ≤ s ≤ 1 − ε is proven for a discretisation
involving piecewise constant functions for the control and piecewise linear for the state.
The derived order of convergence is illustrated by a numerical example.
Using monotone bifunctions, we introduce a recession concept
for general equilibrium problems relying on a variational convergence notion. The interesting purpose is to extend some results of P. L. Lions on
variational problems. In the process we generalize some results by H. Brezis
and H. Attouch relative to the convergence of the resolvents associated with
maximal monotone operators.
A new postprocessing technique suitable for nonuniform triangulations is employed in the sensitivity analysis of some model optimal shape design problems.
Shape optimization is described by finding the geometry of a structure which is optimal in the sense of a minimized cost function with respect to certain constraints. A Newton’s mesh independence principle was very efficiently used to solve a certain class of optimal design problems in [6]. Here motivated by optimization considerations we show that under the same computational cost an even finer mesh independence principle can be given.
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399