A barrier method for constrained nonlinear optimization using a modified Hopfield network

The ability of neural networks to realize some complex nonlinear function makes them attractive for system identification. This paper describes a novel barrier method using artificial neural networks to solve robust parameter estimation problems for nonlinear model with unknown-but-bounded errors and uncertainties. This problem can be represented by a typical constrained optimization problem. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the network convergence to the equilibrium points. A solution for the robust estimation problem with unknown-but-bounded error corresponds to an equilibrium point of the network. Simulation results are presented as an illustration of the proposed approach.

Lower bound to the mass of a relativistic three-boson system in the lightcone

The lower bound masses of the ground-state relativistic three-boson system in 1 + 1, 2 + 1 and 3 + 1 spacetime dimensions are obtained. We have considered a reduction of the ladder Bethe-Salpeter equation to the lightfront in a model with renormalized two-body contact interaction. The lower bounds are deduced with the constraint of reality of the two-boson subsystem mass. It is verified that, in some cases, the lower bound approaches the ground-state binding energy. The corresponding non-relativistic limits are also verified.

Planejamento de Fontes Reativas em Sistemas de Energia Elétrica utilizando a técnica de Decomposição de Benders e o algoritmo de Branch-and-Bound

This paper presents the Benders decomposition technique and Branch and Bound algorithm used in the reactive power planning in electric energy systems. The Benders decomposition separates the planning problem into two subproblems: an investment subproblem (master) and the operation subproblem (slave), which are solved alternately. The operation subproblem is solved using a successive linear programming (SLP) algorithm while the investment subproblem, which is an integer linear programming (ILP) problem with discrete variables, is resolved using a Branch and Bound algorithm especially developed to resolve this type of problem.

On the resolution of the generalized nonlinear complementarity problem

Minimization of a differentiable function subject to box constraints is proposed as a strategy to solve the generalized nonlinear complementarity problem (GNCP) defined on a polyhedral cone. It is not necessary to calculate projections that complicate and sometimes even disable the implementation of algorithms for solving these kinds of problems. Theoretical results that relate stationary points of the function that is minimized to the solutions of the GNCP are presented. Perturbations of the GNCP are also considered, and results are obtained related to the resolution of GNCPs with very general assumptions on the data. These theoretical results show that local methods for box-constrained optimization applied to the associated problem are efficient tools for solving the GNCP. Numerical experiments are presented that encourage the use of this approach.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Scaling predictions for radii of weakly bound triatomic molecules

The mean-square radii of the triatomic molecules 4He 3, 4He 2- 6Li, 4He 2- 7Li, and 4He 2- 23Na were calculated using a renormalized three-body model with a pairwise Dirac-δ interaction, having as physical inputs only the values of the binding energies of the diatomic and triatomic molecules. Molecular three-body systems with bound subsystems were considered. The resultant data were analyzed in detail.

Weakly bound atomic trimers in ultracold traps

The scaling dependence of the recombination parameter as a function of the ratio between the energies of the atomic dimer and the most excited trimer states was derived. The scaling function tends to a unversal function in the limit of zero-range interaction or infinite scattering length. This paper reports on how one can obtain the trimer binding energy of a trapped atomic system, from the three-body recombination rate and the corresponding two-body scattering length.

Three-body recombination in ultracold systems: Prediction of weakly-bound atomic trimer energies

The three-body recombination coefficient of an ultracold atomic system, together with the corresponding two-body scattering length a, allow us to predict the energy E 3 of the shallow trimer bound state, using a universal scaling function. The production of dimers in trapped Bose-Einstein condensates, from three-body recombination processes, in the regime of short magnetic pulses near a Feshbach resonance, is also studied in line with the experimental observation.

A branch-and-bound algorithm for the multi-stage transmission expansion planning

This work presents a branch-and-bound algorithm to solve the multi-stage transmission expansion planning problem. The well known transportation model is employed, nevertheless the algorithm can be extended to hybrid models or to more complex ones such as the DC model. Tests with a realistic power system were carried out in order to show the performance of the algorithm for the expansion plan executed for different time frames. © 2005 IEEE.

Spatial characteristics of borromean, tango, samba and all-bound halo nuclei

We report a renormalized zero-range interaction approach to estimate the size of generic weakly bound three-body systems where two particles are identical. We present results for the neutron-neutron root-mean-square distances of the halo nuclei 6He, 11Li, 14Be and 20C, where the systems are taken as two halo neutrons with an inert point-like core. We also report an approach to obtain the neutron-neutron correlation function in halo nuclei. In this case, our results suggest a review of the corresponding experimental data analysis. © 2007 American Institute of Physics.

Branch and bound algorithm for transmission network expansion planning using DC model

This paper presents an algorithm to solve the network transmission system expansion planning problem using the DC model which is a mixed non-linear integer programming problem. The major feature of this work is the use of a Branch-and-Bound (B&B) algorithm to directly solve mixed non-linear integer problems. An efficient interior point method is used to solve the non-linear programming problem at each node of the B&B tree. Tests with several known systems are presented to illustrate the performance of the proposed method. ©2007 IEEE.

On the bound-state spectrum of a nonrelativistic particle in the background of a short-ranged linear potential

The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N. A. Rao and B. A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in electronics in a simple and transparent way. © Electronic Journal of Theoretical Physics. All rights reserved.

Balance of payments constrained growth within a consistent stock-flow framework: an application to the economies of CARICOM

Includes bibliography

Solution of two-body bound state problems with confining potentials

The homogeneous Lippmann-Schwinger integral equation is solved in momentum space by using confining potentials. Since the confining potentials are unbounded at large distances, they lead to a singularity at small momentum. In order to remove the singularity of the kernel of the integral equation, a regularized form of the potentials is used. As an application of the method, the mass spectra of heavy quarkonia, mesons consisting from heavy quark and antiquark (Υ(bb̄), ψ(cc̄)), are calculated for linear and quadratic confining potentials. The results are in good agreement with configuration space and experimental results. © 2010 American Institute of Physics.

Free time and mixed constrained optimal control problems

We consider free time optimal control problems with pointwise set control constraints u(t) ∈ U(t). Here we derive necessary conditions of optimality for those problem where the set U(t) is defined by equality and inequality control constraints. The main ingredients of our analysis are a well known time transformation and recent results on necessary conditions for mixed state-control constraints. ©2010 IEEE.