A regularized Newton method in electrical impedance tomography using shape Hessian information
A self-adaptive trust region method for the extended linear complementarity problems
By using some NCP functions, we reformulate the extended linear complementarity problem as a nonsmooth equation. Then we propose a self-adaptive trust region algorithm for solving this nonsmooth equation. The novelty of this method is that the trust region radius is controlled by the objective function value which can be adjusted automatically according to the algorithm. The global convergence is obtained under mild conditions and the local superlinear convergence rate is also established under...
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem...
A set oriented approach to global optimal control
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path...
A simple recursive estimator with on-line orthogonalization of the input sequence
A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...
A solution of the continuous Lyapunov equation by means of power series
A structured staircase algorithm for skew-symmetric/symmetric pencils.
A three-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces
We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....
A truncated descent HS conjugate gradient method and its global convergence.
A variant of Newton's method for generalized equations.
A viscosity-proximal gradient method with inertial extrapolation for solving certain minimization problems in Hilbert space
In this paper, we study the strong convergence of the proximal gradient algorithm with inertial extrapolation term for solving classical minimization problem and finding the fixed points of -demimetric mapping in a real Hilbert space. Our algorithm is inspired by the inertial proximal point algorithm and the viscosity approximation method of Moudafi. A strong convergence result is achieved in our result without necessarily imposing the summation condition on the inertial term. Finally, we provide...
Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions
2000 Mathematics Subject Classification: 47H04, 65K10.In this paper we investigate the existence of a sequence (xk ) satisfying 0 ∈ f (xk )+ ∇f (xk )(xk+1 − xk )+ 1/2 ∇2 f (xk )(xk+1 − xk )^2 + G(xk+1 ) and converging to a solution x∗ of the generalized equation 0 ∈ f (x) + G(x); where f is a function and G is a set-valued map acting in Banach spaces.
Adaptive Newton-like method for shape optimization
Adjoint variable method for the study of combined active and passive magnetic shielding.
Algorithmes de type F.A.C. en optimisation convexe
All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound...
Alternating Iteration and Elliptic Variational Inequalities.