On the computation of all eigenvalues for the eigenvalue complementarity problem

In this paper, a parametric algorithm is introduced for computing all eigenvalues for two Eigenvalue Complementarity Problems discussed in the literature. The algorithm searches a finite number of nested intervals \([\bar{l}, \bar{u}]\) in such a way that, in each iteration, either an eigenvalue is computed in \([\bar{l}, \bar{u}]\) or a certificate of nonexistence of an eigenvalue in \([\bar{l}, \bar{u}]\) is provided. A hybrid method that combines an enumerative method [1] and a semi-smooth algorithm [2] is discussed for dealing with the Eigenvalue Complementarity Problem over an interval \([\bar{l}, \bar{u}]\) . Computational experience is presented to illustrate the efficacy and efficiency of the proposed techniques.     

Effective Relaxations and Partitioning Schemes for Solving Water Distribution Network Design Problems to Global Optimality

In this paper, we address the development of a global optimization procedure for the problem of designing a water distribution network, including the case of expanding an already existing system, that satisfies specified flow demands at stated pressure head requirements. The proposed approach significantly improves upon a previous method of Sherali et al. (1998) by way of adopting tighter polyhedral relaxations, and more effective partitioning strategies in concert with a maximal spanning tree-based branching variable selection procedure. Computational experience on three standard test problems from the literature is provided to evaluate the proposed procedure. For all these problems, proven global optimal solutions within a tolerance of 10^–4% and/or within 1$ of optimality are obtained. In particular, the two larger instances of the Hanoi and the New York test networks are solved to global optimality for the very first time in the literature. A new real network design test problem based on the Town of Blacksburg Water Distribution System is also offered to be included in the available library of test cases, and related computational results are presented.     

On the numerical solution of the quadratic eigenvalue complementarity problem

The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices included in its definition. This has been established in a previous paper by reducing a QEiCP of dimension n to a special 2n-order EiCP. In this paper we propose an enumerative algorithm for solving the QEiCP by exploiting this equivalence with an EiCP. The algorithm seeks a global minimum of a special Nonlinear Programming Problem (NLP) with a known global optimal value. The algorithm is shown to perform very well in practice but in some cases terminates with only an approximate optimal solution to NLP. Hence, we propose a hybrid method that combines the enumerative method with a fast and local semi-smooth method to overcome the latter drawback. This algorithm is also shown to be useful for computing a positive eigenvalue for an EiCP under similar assumptions. Computational experience is reported to demonstrate the efficacy and efficiency of the hybrid enumerative method for solving the QEiCP.     

The importance of electron correlation in graphene and hydrogenated graphene

Local density approximation (LDA) and Green function effective Coulomb (GW) calculations are performed to investigate the effect of electronic correlations on the electronic properties of both graphene and graphane. The size of band gap in graphane increases from 3.7 eV in LDA to 4.9 eV in GW approximation. By calculating maximally localized Wannier wave functions, we evaluate the necessary integrals to get the Hubbard U and the exchange J interaction from first principles for both graphene and graphane. Our ab-initio estimates indicate that in the case of graphene, in addition to the hopping amplitude t ～ 2.8 eV giving rise to the Dirac nature of low lying excitations, the Hubbard U value of ～8.7 eV gives rise to a super-exchange strength of J _AFM ～ 3.5 eV. This value dominates over the direct (ferromagnetic) exchange value of J _FM ～ 1.6 eV. This brings substantial Mott-Heisenberg aspects into the problem of graphene. Moreover, similarly large values of the Hubbard and super-exchange strength in graphane suggests that the nature of gap in graphane has substantial Mott character.     

Analytical evaluation of three wild growing Omani medicinal plants

Three wild Omani plants, Moringa peregrina, Acacia nilotica and Rhazya stricta, were selected for the present study. Na, K and Ca contents were determined using flame photometric analysis. M. peregrina seeds (22.5 mg/g) and pods (27.7 mg/g) had higher Na contents than A. nilotica (0.33 mg/g) and R. stricta (0.30 mg/g), whereas the K and Ca contents of R. stricta were significantly higher than those of the other two plants. The protein content was lowest in R. stricta (9.8%) and highest in M peregrina seeds (21.0%). The highest total phenolic contents (TPC) were found in M. peregrina seeds (350.3 mg/g) and the lowest in A. nilotica (66.1 mg/g). The major component of M. peregrina seed oil was oleic acid (74.7%). Gas chromatographic-mass spectrometric analysis (GC-MS) revealed that octadecanal (30.9%) was the major compound in A. nilotica. The presence of various phenolics and flavonoids in M. peregrina, A. nilotica and R. stricta were confirmed by high performance liquid chromatography (HPLC).     

Linear programming based analysis of marginal cost pricing in electric utility capacity expansion

This paper concerns methods for discretizing and approximating the annual load duration curve in the context of a linear programming model and its interpretation in electric utility expansion planning. The emphasis is upon the interpretation of the linear programming dual variables and their relationship with classical results of peak load pricing. In particular, for capacity planning in which one can choose from a diverse number of technological alternatives, we support the work of Wenders by precisely characterizing how off-peak periods bear partial responsibility of the capacity cost.     

On the convergence of cutting plane algorithms for a class of nonconvex mathematical programs

We discuss the convergence of cutting plane algorithms for a class of nonconvex programs called the Generalized Lattice Point Problems (GLPP). A set of sufficient conditions which guarantee finite convergence are presented. Although these conditions are usually difficult to enforce in a practical implementation, they do illustrate the various factors that must be involved in a convergent rudimentary cutting plane algorithm. A striking example of nonconvergence (in which no subsequence converges to a feasible solution, even when seemingly strong cutting planes are used), is presented to show the effect of neglecting one such factor. We give an application of our analysis to problems with multiple choice constraints and finally discuss a modification of cutting plane algorithms so as to make finite convergence more readily implementable.