In this paper, the common centralized DEA models are extended to the bi-level centralized resource allocation (CRA) models based on revenue efficiency. Based on the Karush–Kuhn–Tucker (KKT) conditions, the bi-level CRA model is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). A recurrent neural network is developed for solving this one-level mathematica...

Avery, 0. T. & Goebel, W. F. (1929). J. exp. Med. 50, 533. Bates, F. J. (1942). Polarimetry, Saccharimetry and the Sugare, pp. 493, 494. Washington, D.C.: United States Government Printing Office. Beiser, S. M., Burke, G. C. & Tanenbaum, S. W. (1960). J. molec. Biol. 2, 125. Fischer, E. (1910). Ber. dtsch. chem. Ge8. 48, 2534. Goebel, W. F., Avery, 0. T. & Babers, F. H. (1934). J. exp. Med. 60,...

The aim of this paper is to study first order optimality conditions for ideal efficient points in the Löwner partial order, when the data functions of the minimization problem are differentiable and convex with respect to the cone of symmetric semidefinite matrices. We develop two sets of first order necessary and sufficient conditions. The first one, formally very similar to the classical Karu...

In this article, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and gener...

We study the Celis-Dennis-Tapia (CDT) problem: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that occurs when the Hessian of the Lagrangian is indefinit...

The positive semidefinite rank of a convex body C is the size of its smallest positive semidefinite formulation. We show that the positive semidefinite rank of any convex body C is at least √ log d where d is the smallest degree of a polynomial that vanishes on the boundary of the polar of C. This improves on the existing bound which relies on results from quantifier elimination. Our proof reli...

In this paper, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and general...

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

train energy saving problem investigates how to control train's velocity such that the quantity of energy consumption is minimized and some system constraints are satis ed. on the assumption that the train's weights on different links are estimated by fuzzy variables when making the train scheduling strategy, we study the fuzzy train energy saving problem. first, we propose a fuzzy energy ...