A note on optimality conditions for the Euclidean. Multifacility location problem

Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares problem with bounds on the Euclidean norms of certain subvectors.     

On variational approximations in quantum molecular dynamics

The Dirac-Frenkel-McLachlan variational principle is the basic tool for obtaining computationally accessible approximations in quantum molecular dynamics. It determines equations of motion for an approximate time-dependent wave function on an approximation manifold of reduced dimension. This paper gives a near-optimality result for variational approximations. It bounds the error in terms of the distance of the exact wave function to the approximation manifold and identifies the parameters that control the deviation of the variational approximation from the best approximation on the manifold.

     

A fast Pareto genetic algorithm approach for solving expensive multiobjective optimization problems

We present a new multiobjective evolutionary algorithm (MOEA), called fast Pareto genetic algorithm (FastPGA), for the simultaneous optimization of multiple objectives where each solution evaluation is computationally- and/or financially-expensive. This is often the case when there are time or resource constraints involved in finding a solution. FastPGA utilizes a new ranking strategy that utilizes more information about Pareto dominance among solutions and niching relations. New genetic operators are employed to enhance the proposed algorithm’s performance in terms of convergence behavior and computational effort as rapid convergence is of utmost concern and highly desired when solving expensive multiobjective optimization problems (MOPs). Computational results for a number of test problems indicate that FastPGA is a promising approach. FastPGA yields similar performance to that of the improved nondominated sorting genetic algorithm (NSGA-II), a widely-accepted benchmark in the MOEA research community. However, FastPGA outperforms NSGA-II when only a small number of solution evaluations are permitted, as would be the case when solving expensive MOPs.     

Optimal birth control of age-dependent competitive species III. Overtaking problem

A study is made of an overtaking optimal problem for a population system consisting of two competing species, which is controlled by fertilities. The existence of optimal policy is proved and a maximum principle is carefully derived under less restrictive conditions. Weak and strong turnpike properties of optimal trajectories are established.     

Alternative proof and interpretations for a recent state-dependent importance sampling scheme

Recently, a state-dependent change of measure for simulating overflows in the two-node tandem queue was proposed by Dupuis et al. (Ann. Appl. Probab. 17(4):1306–1346, 2007), together with a proof of its asymptotic optimality. In the present paper, we present an alternative, shorter and simpler proof. As a side result, we obtain interpretations for several of the quantities involved in the change of measure in terms of likelihood ratios. Part of this research has been funded by the Dutch BSIK/BRICKS project; part of this research was done while the first author was visiting INRIA/IRISA, Rennes, France.     

On a constructive approach to optimality conditions for convex SIP problems with polyhedral index sets

In the paper, we consider a problem of convex Semi-Infinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new optimality conditions with other known results is provided.     

一类海冰-海水耦合热力学系统参数辨识问题的最优性

针对一维的海冰-海水耦合热力学系统,以该系统中的物理参数为辨识量,以温度偏差为目标函数,建立了一个参数辨识模型,并证明了该问题最优解的存在性,从而为这类海冰-海水耦合热力学系统参数辨识问题的数值计算提供数学理论依据.