Augmented Lagrangian Algorithms Based on the Spectral Projected Gradient Method for Solving Nonlinear Programming Problems

The spectral projected gradient method SPG is an algorithm for large-scale bound-constrained optimization introduced recently by Birgin, Martínez, and Raydan. It is based on the Raydan unconstrained generalization of the Barzilai-Borwein method for quadratics. The SPG algorithm turned out to be surprisingly effective for solving many large-scale minimization problems with box constraints. Therefore, it is natural to test its perfomance for solving the sub-problems that appear in nonlinear programming methods based on augmented Lagrangians. In this work, augmented Lagrangian methods which use SPG as the underlying convex-constraint solver are introduced (ALSPG) and the methods are tested in two sets of problems. First, a meaningful subset of large-scale nonlinearly constrained problems of the CUTE collection is solved and compared with the perfomance of LANCELOT. Second, a family of location problems in the minimax formulation is solved against the package FFSQP.     

On Hyperbolic Variational Inequalities of First Order and Some Applications

This paper presents further developments in the study of strong solutions and their coincidence sets to the obstacle problem for linear transport operators. Under natural mild assumptions, the strong convergence of the solutions and the characteristic functions of their coincidence sets is obtained in the passage of second order to first order problems. An application to a steady-state chemotaxis problem is given. The extension to the two obstacles problem of first order is also presented, having in view an application to a porous media model in presence of saturation arising in petroleum engineering.     

New heuristics for over-constrained flight to gate assignments

We consider the over-constrained Airport Gate Assignment Problem where the number of flights exceed the number of gates available, and where the objectives are to minimize the number of ungated flights and the total walking distances. The problem is formulated as a binary quadratic programming problem. We design a greedy algorithm and use a Tabu Search meta-heuristic to solve the problem. The greedy algorithm minimizes ungated flights while we devise a new neighbourhood search technique, the Interval Exchange Move, which allows us flexibility in seeking good solutions, especially when flight schedules are dense in time. Experiments conducted give good results.     

Crossdocking—JIT scheduling with time windows

In this paper, we study a problem central to crossdocking that aims to eliminate or minimize storage and order picking activity using JIT scheduling. The problem is modelled naturally as a machine scheduling problem. As the problem is NP-hard, and for real-time applications, we designed and implemented two heuristics. The first uses Squeaky Wheel Optimization embedded in a Genetic Algorithm and the second uses Linear Programming within a Genetic Algorithm. Both heuristics offer good solutions in experiments where comparisons are made with the CPLEX solver.     

Dirac-Hestenes spinor fields on Riemann-Cartan manifolds

In this paper we study Dirac-Hestenes spinor fields (DHSF) on a four-dimensional Riemann-Cartan spacetime (RCST). We prove that these fields must be defined as certain equivalence classes of even sections of the Clifford bundle (over the RCST), thereby being certain particular sections of a new bundle named the spin-Clifford bundle (SCB). The conditions for the existence of the SCB are studied and are shown to be equivalent to Geroch's theorem concerning the existence of spinor structures in a Lorentzian spacetime. We introduce also the covariant and algebraic Dirac spinor fields and compare these with DHSF, showing that all three kinds of spinor fields contain the same mathematical and physical information. We clarify also the notion of (Crumeyrolle's) amorphous spinors (Dirac-Kähler spinor fields are of this type), showing that they cannot be used to describe fermionic fields. We develop a rigorous theory for the covariant derivatives of Clifford fields (sections of the Clifford bundle, CB) and of Dirac-Hestenes spinor fields. We show how to generalize the original Dirac-Hestenes equation in Minkowski spacetime for the case of RCST. Our results are obtained from a variational principle formulated through the multiform derivative approach to Lagrangian field theory in the Clifford bundle.     

Necessary conditions and non-existence results for autonomous nonconvex variational problems

Classical one-dimensional, autonomous Lagrange problems are considered. In absence of any smoothness, convexity or coercivity condition on the energy density, we prove a DuBois-Reymond type necessary condition, expressed as a differential inclusion involving the subdifferential of convex analysis. As a consequence, a non-existence result is obtained.     

Primitive rispetto all’ oscillazione

We study the real valued functions having a primitive with respect to the oscillation or a primitive with respect to the oscillation up to anegligible set.

---

---

Supported by MURST of Italy.     

Impact of photodepletion to amplified spontaneous emission of proton-transfer dyes in polymeric matrices

A six level rate equation system was used to investigate the impact of photodepletion to amplified spontaneous emission (ASE) of intramolecular proton-transfer (IPT) dyes incorporated into polymeric hosts. The model includes the most important transitions for the normal and tautomer form of the molecule as well as intersystem crossing and triplet–triplet transitions. The experimentally observed pulse shape as well as photodepletion phenomena, i.e. a first order exponential decay of the ASE intensity and a shortening in ASE pulse width, have been simulated successfully. Additionally, the model was used to propose an explanation of the unexpected high photodepletion of proton-transfer dyes in solids. The results show that the emission cross section and reabsorption cross section of the tautomer form of the molecule are the most important parameter not only for efficiency but also for photodepletion. The model was tested by comparison with experimental results of 2-(2’-hydroxyphenyl)benzimidazole in polymethylmethacrylate (PMMA), polystyrene (PS) and a 1:1 alternating copolymer matrix PS-co-PMMA. PACS 78.45.th; 42.55.Mv; 42.70.Jk     

A Genetic Algorithm for Solving a Capacitated p-Median Problem

Facility-location problems have several applications, such as telecommunications, industrial transportation and distribution. One of the most well-known facility-location problems is the p-median problem. This work addresses an application of the capacitated p-median problem to a real-world problem. We propose a genetic algorithm (GA) to solve the capacitated p-median problem. The proposed GA uses not only conventional genetic operators, but also a new heuristic “hypermutation” operator suggested in this work. The proposed GA is compared with a tabu search algorithm.