A Family of Mixed Finite Elements for the Elasticity Problem.
A fast Lagrangian heuristic for large-scale capacitated lot-size problems with restricted cost structures
In this paper, we demonstrate the computational consequences of making a simple assumption on production cost structures in capacitated lot-size problems. Our results indicate that our cost assumption of increased productivity over time has dramatic effects on the problem sizes which are solvable. Our experiments indicate that problems with more than 1000 products in more than 1000 time periods may be solved within reasonable time. The Lagrangian decomposition algorithm we use does of course not...
A finite dimensional linear programming approximation of Mather's variational problem
We provide an approximation of Mather variational problem by finite dimensional minimization problems in the framework of Γ-convergence. By a linear programming interpretation as done in [Evans and Gomes, ESAIM: COCV 8 (2002) 693–702] we state a duality theorem for the Mather problem, as well a finite dimensional approximation for the dual problem.
A fixed point formulation of the -means algorithm and a connection to Mumford-Shah.
A General Convergence Theorem for the Reduced Gradient Method.
A Generalization of the Potential Method for Conditional Maxima on the Banach, Reflexive Spaces.
A Generalized Conjugate Gradient Algorithm for Minimization.
A generalized limited-memory BNS method based on the block BFGS update
A block version of the BFGS variable metric update formula is investigated. It satisfies the quasi-Newton conditions with all used difference vectors and gives the best improvement of convergence in some sense for quadratic objective functions, but it does not guarantee that the direction vectors are descent for general functions. To overcome this difficulty and utilize the advantageous properties of the block BFGS update, a block version of the limited-memory BNS method for large scale unconstrained...
A global method for some class of optimization and control problems.
A Globalization Scheme for the Generalized Gauss-Newton Method.
A globally convergent non-interior point algorithm with full Newton step for second-order cone programming
A non-interior point algorithm based on projection for second-order cone programming problems is proposed and analyzed. The main idea of the algorithm is that we cast the complementary equation in the primal-dual optimality conditions as a projection equation. By using this reformulation, we only need to solve a system of linear equations with the same coefficient matrix and compute two simple projections at each iteration, without performing any line search. This algorithm can start from an arbitrary...
A heuristic algorithm for the flowshop scheduling problem
A hybrid inertial projection-proximal method for variational inequalities.
A hybrid iterative scheme for equilibrium problems, variational inequality problems, and fixed point problems in Banach spaces.
A hybrid method for nonlinear least squares that uses quasi-Newton updates applied to an approximation of the Jacobian matrix
In this contribution, we propose a new hybrid method for minimization of nonlinear least squares. This method is based on quasi-Newton updates, applied to an approximation of the Jacobian matrix , such that . This property allows us to solve a linear least squares problem, minimizing instead of solving the normal equation , where is the required direction vector. Computational experiments confirm the efficiency of the new method.
A least-squares method for the numerical solution of the Dirichlet problem for the elliptic monge − ampère equation in dimension two
We address in this article the computation of the convex solutions of the Dirichlet problem for the real elliptic Monge − Ampère equation for general convex domains in two dimensions. The method we discuss combines a least-squares formulation with a relaxation method. This approach leads to a sequence of Poisson − Dirichlet problems and another sequence of low dimensional algebraic eigenvalue problems of a new type. Mixed finite element approximations with a smoothing procedure are used for the...
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part II.
A Method of Solving Nonlinear Variational Problems by Nonlinear Transformation of the Objective Functional. Part I.
A minimum effort optimal control problem for elliptic PDEs
This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation...
A minimum effort optimal control problem for elliptic PDEs
This work is concerned with a class of minimum effort problems for partial differential equations, where the control cost is of L∞-type. Since this problem is non-differentiable, a regularized functional is introduced that can be minimized by a superlinearly convergent semi-smooth Newton method. Uniqueness and convergence for the solutions to the regularized problem are addressed, and a continuation strategy based on a model function is proposed. Numerical examples for a convection-diffusion equation...