The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the secondorder sufficient condition for optimality...

In this paper, we study the existence and stability of travelling wave solutions of a kinetic reactiontransport equation. The model describes particles moving according to a velocity-jump process, and proliferating thanks to a reaction term of monostable type. The boundedness of the velocity set appears to be a necessary and sufficient condition for the existence of positive travelling waves. T...

A class of algorithms are described for the minimization of a function of n variables subject to linear inequality constraints. Under weak conditions convergence to a stationary point is demonstrated. The method uses a mixture of conjugate direction constructing and accelerating steps. Any mixture, for example alternation, may be used provided that the subsequence of conjugate direction constru...

In this paper some Newton and quasi-Newton algorithms for the solution of inequality constrained minimization problems are considered. All the algorithms described produce sequences fx k g converging q-superlinearly to the solution. Furthermore , under mild assumptions, a q-quadratic convergence rate in x is also attained. Other features of these algorithms are that the solution of linear syste...

We consider the problem of optimizing the strongly convex sum of a finite number of convex functions. Standard algorithms for solving this problem in the class of incremental/stochastic methods have at most a linear convergence rate. We propose a new incremental method whose convergence rate is superlinear – the Newtontype incremental method (NIM). The idea of the method is to introduce a model...

In this paper, we establish the local superlinear convergence property of some polynomialtime interior-point methods for an important family of conic optimization problems. The main structural property used in our analysis is the logarithmic homogeneity of self-concordant barrier function, which must have negative curvature. We propose a new path-following predictor-corrector scheme, which work...

Copyright q 2010 I. Rachůnková and J. Tomeček. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The paper studies the singular differential equation p t u′ ′ p t f u , which has a singularity at t 0. Here the existence of strictly ...

When N processors perform depth-first search on-disjoint parts of a state space tree to find a solution, the speedup can be superlinear (i.e., > N) or sublinear (i.e., < N) depending upon when a solution is first encountered in the space by one of the processors. It may appear that on the average, the speedup would be either linear or sublinear. Using an analytical model, we show that if the se...

This paper first surveys the near-total lack of superlinear lower bounds in complexity theory, for “natural” computational problems with respect to many models of computation. We note that the dividing line between models where such bounds are known and those where none are known comes when the model allows non-local communication with memory at unit cost . We study a model that imposes a “fair...