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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...
We describe an algorithm for computing the value function for “all source, single destination” discrete-time nonlinear optimal control problems together with approximations of associated globally optimal control strategies. The method is based on a set oriented approach for the discretization of the problem in combination with graph-theoretic techniques. The central idea is that a discretization of phase space of the given problem leads to an (all source, single destination) shortest path problem...
We describe an algorithm for computing the value function for “all
source, single destination” discrete-time nonlinear optimal control
problems together with approximations of associated globally optimal
control strategies. The method is based on a set oriented approach
for the discretization of the problem in combination with
graph-theoretic techniques. The central idea is that a
discretization of phase space of the given problem leads to an (all
source, single destination) shortest path...
Editorial from the Editor-in-Chief regarding this case of plagiarismPhilippe Mahey 1 Introduction
Plagiarism
is a plague that any scientific publication in any discipline should fight and
eradicate all over the world. Unfortunately, if, on the one hand, the powerful
search engines available on the web have helped referees to identify most of
the cases, the increasing number of publications have on the other hand
facilitated that dubious practice and the number of cases have increased.
The case...
A simple proof is given of a Monge-Kantorovich duality theorem for a lower bounded lower semicontinuous cost function on the product of two completely regular spaces. The proof uses only the Hahn-Banach theorem and some properties of Radon measures, and allows the case of a bounded continuous cost function on a product of completely regular spaces to be treated directly, without the need to consider intermediate cases. Duality for a semicontinuous cost function is then deduced via the use of an...
In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that...
In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore,...
A smoothing sample average approximation (SAA) method based on the log-exponential function is proposed for solving a stochastic mathematical program with complementarity constraints (SMPCC) considered by Birbil et al. (S. I. Birbil, G. Gürkan, O. Listes: Solving stochastic mathematical programs with complementarity constraints using simulation, Math. Oper. Res. 31 (2006), 739–760). It is demonstrated that, under suitable conditions, the optimal solution of the smoothed SAA problem converges almost...
Alignment of sequences is widely used for biological sequence comparisons, and only biological events like mutations, insertions and deletions are considered. Other biological events like inversions are not automatically detected by the usual alignment algorithms, thus some alternative approaches have been tried in order to include inversions or other kinds of rearrangements. Despite many important results in the last decade, the complexity of the problem of alignment with inversions is still unknown....
Alignment of sequences is widely used for biological sequence
comparisons, and only biological events like mutations, insertions
and deletions are considered. Other biological events like
inversions are not automatically detected by the usual alignment
algorithms, thus some alternative approaches have been tried in order
to include inversions or other kinds of rearrangements.
Despite many important results in the last decade, the complexity of the
problem of alignment with inversions is...
In this short paper, we are concerned with the stability of nonlinear bilevel programs. A stability problem is proven and an example is given to illustrate this theorem.
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