On the approximation of inconsistent inequality systems.
On the best choice of a damping sequence in iterative optimization methods.
Some iterative methods of mathematical programming use a damping sequence {αt} such that 0 ≤ αt ≤ 1 for all t, αt → 0 as t → ∞, and Σ αt = ∞. For example, αt = 1/(t+1) in Brown's method for solving matrix games. In this paper, for a model class of iterative methods, the convergence rate for any damping sequence {αt} depending only on time t is computed. The computation is used to find the best damping sequence.
On the boundary element method for the Signorini problem of the Laplacian.
On the computer algebra implementation of the least squares method on the nonnegative orthant.
On the continuous dependence of trajectories of bilinear systems on controls and its applications
On the control of a truncated general immigration process through the introduction of a predator.
On the convergence of modified relaxation methods for extremum problems
On the convergence of SCF algorithms for the Hartree-Fock equations
The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.
On the convergence of some methods for variational inclusions
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite difference...
On the convergence rate of approximation schemes for Hamilton-Jacobi-Bellman Equations
Using systematically a tricky idea of N.V. Krylov, we obtain general results on the rate of convergence of a certain class of monotone approximation schemes for stationary Hamilton-Jacobi-Bellman equations with variable coefficients. This result applies in particular to control schemes based on the dynamic programming principle and to finite difference schemes despite, here, we are not able to treat the most general case. General results have been obtained earlier by Krylov for finite...
On the convergence rate of empirical estimates in chance constrained stochastic programming
On the convergence rate of regularization methods for ill-posed extremal problems
On the decrease of a quadratic function along the projected-gradient path.
On the degree of asymmetry in the travelling salesman problem
On the Efficient Solution of Nonlinear Finite Element Equations. II. Bound-Constrained Problems.
On the Efficient Solution of Nonlinear Finite Element Equations I.
On the efficient update of rectangular LU-factorizations subject to low rank modifications.
On the generalized Riccati matrix differential equation. Exact, approximate solutions and error estimate
In this paper explicit expressions for solutions of Cauchy problems and two-point boundary value problems concerned with the generalized Riccati matrix differential equation are given. These explicit expressions are computable in terms of the data and solutions of certain algebraic Riccati equations related to the problem. The interplay between the algebraic and the differential problems is used in order to obtain approximate solutions of the differential problem in terms of those of the algebraic...