Saddle Points and Multiple Solutions of Differential Equations.
Self-adaptive implicit methods for monotone variant variational inequalities.
Semilinear evolution equations of second order via maximal regularity.
Semi-smooth Newton methods for the Signorini problem
Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.
Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations
AMS Subj. Classification: 49J15, 49M15The control problem of minimal time transition between two stationary points are formulated in a framework of an indirect numerical method. The problem is regularized and the monotone behavior of the regularisation procedure is investigated. Semi-smooth Newton method applied on the regularized problems converge superlinearly and usually produce a very accurate solution. Differently from other methods, this one does not need a-priory knowledge of the control switching...
Shape optimization by means of the penalty method with extrapolation
A model shape optimal design in is solved by means of the penalty method with extrapolation, which enables to obtain high order approximations of both the state function and the boundary flux, thus offering a reliable gradient for the sensitivity analysis. Convergence of the proposed method is proved for certain subsequences of approximate solutions.
Shape optimization in contact problems based on penalization of the state inequality
The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.
Sharp upper global a posteriori error estimates for nonlinear elliptic variational problems
The paper is devoted to the problem of verification of accuracy of approximate solutions obtained in computer simulations. This problem is strongly related to a posteriori error estimates, giving computable bounds for computational errors and detecting zones in the solution domain where such errors are too large and certain mesh refinements should be performed. A mathematical model embracing nonlinear elliptic variational problems is considered in this work. Based on functional type estimates developed...
Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods
The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each...
Solution for a classical problem in the calculus of variations via rationalized Haar functions
A numerical technique for solving the classical brachistochrone problem in the calculus of variations is presented. The brachistochrone problem is first formulated as a nonlinear optimal control problem. Application of this method results in the transformation of differential and integral expressions into some algebraic equations to which Newton-type methods can be applied. The method is general, and yields accurate results.
Solution of a class of quasilinear Dirichlet and Neumann problems by the method of reduction.
Solution of a class of quasilinear Dirichlet and Neumann problems by the method of reduction. (Short Communication).
Solvability and numerical algorithms for a class of variational data assimilation problems
A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.
Solvability and numerical algorithms for a class of variational data assimilation problems
A class of variational data assimilation problems on reconstructing the initial-value functions is considered for the models governed by quasilinear evolution equations. The optimality system is reduced to the equation for the control function. The properties of the control equation are studied and the solvability theorems are proved for linear and quasilinear data assimilation problems. The iterative algorithms for solving the problem are formulated and justified.
Solvability of the power flow problem in DC overhead wire circuit modeling
Proper traffic simulation of electric vehicles, which draw energy from overhead wires, requires adequate modeling of traction infrastructure. Such vehicles include trains, trams or trolleybuses. Since the requested power demands depend on a traffic situation, the overhead wire DC electrical circuit is associated with a non-linear power flow problem. Although the Newton-Raphson method is well-known and widely accepted for seeking its solution, the existence of such a solution is not guaranteed. Particularly...
Some applications of optimal control theory of distributed systems
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
Some Applications of Optimal Control Theory of Distributed Systems
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
Some Krasnonsel'skiĭ-Mann algorithms and the multiple-set split feasibility problem. (Some Krasnosel'skiĭ-Mann algorithms and the multiple-set split feasibility problem.)
Special issue on decentralized control of large scale complex systems
This special issue provides information on current and future research directions in the emerging field of Decentralized Control of Large Scale Complex Systems. There is generally adopted view that a dynamic system is large scale complex whenever it is necessary to partition its analysis or synthesis problem to manageable subproblems. Its fundamental characteristics in modeling and control are high dimensionality, uncertainty, information structure constraints, and delays. Theory of large scale...
Stability of saddle point problems with penalty