Numerical solution of PDE optimal control problems involving affine pointwise control constraints is investigated. Optimality conditions are derived and a semi-smooth Newton method is presented. Global and local superlinear convergence of the method are obtained for linear problems. Differently from box constraints, in the case of general affine constraints a proper weighting of the control cos...

Inherent parallelism is regarded as one of the most important advantages of evolutionary algorithms. This paper aims at makin g an initial study on the speedup of scalable parallel evolutionary algorithms. First the scalable parallel evolutionary algo rithms are described; then the speedup of such scalable algorithms is defined based on the first hitting time; Using the new definition, the rela...

Quantitative bounds are presented for the superlinear convergence of the MINRES method of Paige and Saunders [SIAM J. Numer. Anal., 1975] for the solution of sparse linear systems Ax = b, with A symmetric and indefinite. It is shown that the superlinear convergence is observed as soon as the harmonic Ritz values approximate well the eigenvalues of A that are either closest to zero or farthest f...

We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form:

In this note we establish multiple solutions for a semilinear elliptic equation with superlinear nonlinearility without assuming any symmetry.

An SQP algorithm is presented for solving constrained nonlinear programming problems. The algorithm uses three stepsize strategies in order to achieve global and superlinear convergence. Switching rules are implemented that combine the merits and avoid the drawbacks of the three stepsize strategies. A penalty parameter is determined using an adaptive strategy that aims to achieve sufficient dec...