A Constraint Linearization Method for Nondifferentiable Convex Minimization.
A contribution to methods of Exterior Penalty Functions for Nonlinear Programming
A hybrid algorithm for solving inverse problems in elasticity
A new method for solving monotone generalized variational inequalities.
A new regular multiplier embedding
Embedding approaches can be used for solving non linear programs P. The idea is to define a one-parametric problem such that for some value of the parameter the corresponding problem is equivalent to P. A particular case is the multipliers embedding, where the solutions of the corresponding parametric problem can be interpreted as the points computed by the multipliers method on P. However, in the known cases, either path-following methods can not be applied or the necessary conditions for its convergence...
A Note on Embeddings for the Augmented Lagrange Method
A note on the usage of nondifferentiable exact penalties in some special optimization problems
A penalty method for deriving necessary conditions in problems of optimal control
A penalty method for topology optimization subject to a pointwise state constraint
This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.
A Posteriori Error Estimation for Reduced Order Solutions of Parametrized Parabolic Optimal Control Problems
We consider the efficient and reliable solution of linear-quadratic optimal control problems governed by parametrized parabolic partial differential equations. To this end, we employ the reduced basis method as a low-dimensional surrogate model to solve the optimal control problem and develop a posteriori error estimation procedures that provide rigorous bounds for the error in the optimal control and the associated cost functional. We show that our approach can be applied to problems involving...
A sequential iteration algorithm with non-monotoneous behaviour in the method of projections onto convex sets
The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in a Euclidean space, may lead to slow convergence of the constructed sequence when that sequence enters some narrow “corridor” between two or more convex sets. A way to leave such corridor consists in taking a big step at different moments during the iteration, because in that way the monotoneous behaviour that is responsible for the slow convergence may be interrupted. In this...
Absolute minimizer in convex programming by exponential penalty.
An algorithm for construction of ε-value functions for the Bolza control problem
The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an ε-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an ε-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper...
An implicit extragradient method for hierarchical variational inequalities.
An Ishikawa-hybrid proximal point algorithm for nonlinear set-valued inclusions problem based on -accretive framework.
Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as is examined.
Analysis and finite element error estimates for the velocity tracking problem for Stokes flows via a penalized formulation
A distributed optimal control problem for evolutionary Stokes flows is studied via a pseudocompressibility formulation. Several results concerning the analysis of the velocity tracking problem are presented. Semidiscrete finite element error estimates for the corresponding optimality system are derived based on estimates for the penalized Stokes problem and the BRR (Brezzi-Rappaz-Raviart) theory. Finally, the convergence of the solutions of the penalized optimality systems as ε → 0 is examined. ...
Approximate gradient projection method with general Runge-Kutta schemes and piecewise polynomial controls for optimal control problems
Approximation methods for nonlinear problems with constraints in form of variational inequalities
Area of contraction of Newton's method applied to a penalty technique for obstacle problems