On the stability of the optimal value and the optimal set in optimization problems

The paper develops a stability theory for the optimal value and the optimal set mapping of optimization problems posed in a Banach space. The problems considered in this paper have an arbitrary number of inequality constraints involving lower semicontinuous (not necessarily convex) functions and one closed abstract constraint set. The considered perturbations lead to problems of the same type as the nominal one (with the same space of variables and the same number of constraints), where the abstract constraint set can also be perturbed. The spaces of functions involved in the problems (objective and constraints) are equipped with the metric of the uniform convergence on the bounded sets, meanwhile in the space of closed sets we consider, coherently, the Attouch-Wets topology. The paper examines, in a unified way, the lower and upper semicontinuity of the optimal value function, and the closedness, lower and upper semicontinuity (in the sense of Berge) of the optimal set mapping. This paper can be seen as a second part of the stability theory presented in [17], where we studied the stability of the feasible set mapping (completed here with the analysis of the Lipschitz-like property).

An Analysis of black-box optimization problems in reinsurance: evolutionary-based approaches

Black-box optimization problems (BBOP) are de ned as those optimization problems in which the objective function does not have an algebraic expression, but it is the output of a system (usually a computer program). This paper is focussed on BBOPs that arise in the eld of insurance, and more speci cally in reinsurance problems. In this area, the complexity of the models and assumptions considered to de ne the reinsurance rules and conditions produces hard black-box optimization problems, that must be solved in order to obtain the optimal output of the reinsurance. The application of traditional optimization approaches is not possible in BBOP, so new computational paradigms must be applied to solve these problems. In this paper we show the performance of two evolutionary-based techniques (Evolutionary Programming and Particle Swarm Optimization). We provide an analysis in three BBOP in reinsurance, where the evolutionary-based approaches exhibit an excellent behaviour, nding the optimal solution within a fraction of the computational cost used by inspection or enumeration methods.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

An axiomatic justification of mediation in bankruptcy problems.

This paper provides a natural way of reaching an agreement between two prominent proposals in a bankruptcy problem. Particularly, using the fact that such problems can be faced from two different points of views, awards and losses, we justify the average of any pair of dual bankruptcy rules through the definition a double recursive process. Finally, by considering three posible sets of equity principles that a particular society may agree on, we retrieve the average of old and well known bankruptcy rules, the Constrained Equal Awards and the Constrained Equal Losses rules, Piniles’ rule and its dual rule, and the Constrained Egalitarian rule and its dual rule. Keywords: Bankruptcy problems, Midpoint, Bounds, Duality, Recursivity. JEL classification: C71, D63, D71.

Solidarity and uniform rules in bankruptcy problems

The idea of ensuring a guarantee (a minimum amount of the resources) to each agent has recently acquired great relevance, in both social and politi- cal terms. Furthermore, the notion of Solidarity has been treated frequently in redistribution problems to establish that any increment of the resources should be equally distributed taking into account some relevant characteris- tics. In this paper, we combine these two general concepts, guarantee and solidarity, to characterize the uniform rules in bankruptcy problems (Con- strained Equal Awards and Constrained Equal Losses rules). Keywords: Constrained Equal Awards, Constrained Equal Losses, Lower bounds, Bankruptcy problems, Solidarity. JEL classification: C71, D63, D71.

A New Approach for Bounding Awards in Bankruptcy Problems

The solution for the ‘Contested Garment Problem’, proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the demand overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of bankruptcy problems from its beginning (O’Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of ‘Commonly Accepted Equity Principles’, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the estate, we analyze its recursive application for different sets of equity principles. Keywords: Bankruptcy problems, Bankruptcy rules, Lower bounds, Recursive process

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Sequential decisions in allocation problems

[eng] In the context of cooperative TU-games, and given an order of players, we consider the problem of distributing the worth of the grand coalition as a sequentia decision problem. In each step of process, upper and lower bounds for the payoff of the players are required related to successive reduced games. Sequentially compatible payoffs are defined as those allocation vectors that meet these recursive bounds. The core of the game is reinterpreted as a set of sequentally compatible payoffs when the Davis-Maschler reduced game is considered (Th.1). Independently of the reduction, the core turns out to be the intersections of the family of the sets of sequentially compatible payoffs corresponding to the different possible orderings (Th.2), so it is in some sense order-independent. Finally, we analyze advantagenous properties for the first player

Decentralization in Croatia: problems and possible solutions

El 2001 Croàcia va posar en marxa la iniciativa destinada a afluixar un alt grau de centralització mitjançant l'ampliació dels mandats de les unitats locals i el canvi de les fonts de finançament de les funcions públiques. No obstant això, els passos inicials en el procés de descentralització no ha estat seguida per altres mesures de descentralització fiscal, i en conseqüència, el seu nivell s'ha mantingut pràcticament sense canvis. El treball es proposa elaborar els principals problemes i obstacles en relació amb l'aplicació efectiva del procés de descentralització i donar tres grups de propostes per a la descentralització: (i) la divisió dels poders obligatoris entre les diferents unitats locals, (ii) el canvi en el finançament i (Iii) modificar la divisió territorial del país.

Improving the risk concept: a revision of Arrow-Pratt theory in the context of controlled dynamic stochastic environments

In the literature on risk, one generally assume that uncertainty is uniformly distributed over the entire working horizon, when the absolute risk-aversion index is negative and constant. From this perspective, the risk is totally exogenous, and thus independent of endogenous risks. The classic procedure is "myopic" with regard to potential changes in the future behavior of the agent due to inherent random fluctuations of the system. The agent's attitude to risk is rigid. Although often criticized, the most widely used hypothesis for the analysis of economic behavior is risk-neutrality. This borderline case must be envisaged with prudence in a dynamic stochastic context. The traditional measures of risk-aversion are generally too weak for making comparisons between risky situations, given the dynamic �complexity of the environment. This can be highlighted in concrete problems in finance and insurance, context for which the Arrow-Pratt measures (in the small) give ambiguous.

The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

A multi-objective model for a multi-period distribution management problem

The problems arising in commercial distribution are complex and involve several players and decision levels. One important decision is relatedwith the design of the routes to distribute the products, in an efficient and inexpensive way.This article deals with a complex vehicle routing problem that can beseen as a new extension of the basic vehicle routing problem. The proposed model is a multi-objective combinatorial optimization problemthat considers three objectives and multiple periods, which models in a closer way the real distribution problems. The first objective is costminimization, the second is balancing work levels and the third is amarketing objective. An application of the model on a small example, with5 clients and 3 days, is presented. The results of the model show the complexity of solving multi-objective combinatorial optimization problems and the contradiction between the several distribution management objective.

Strong minimax lower bounds for learning

Minimax lower bounds for concept learning state, for example, thatfor each sample size $n$ and learning rule $g_n$, there exists a distributionof the observation $X$ and a concept $C$ to be learnt such that the expectederror of $g_n$ is at least a constant times $V/n$, where $V$ is the VC dimensionof the concept class. However, these bounds do not tell anything about therate of decrease of the error for a {\sl fixed} distribution--concept pair.\\In this paper we investigate minimax lower bounds in such a--stronger--sense.We show that for several natural $k$--parameter concept classes, includingthe class of linear halfspaces, the class of balls, the class of polyhedrawith a certain number of faces, and a class of neural networks, for any{\sl sequence} of learning rules $\{g_n\}$, there exists a fixed distributionof $X$ and a fixed concept $C$ such that the expected error is larger thana constant times $k/n$ for {\sl infinitely many n}. We also obtain suchstrong minimax lower bounds for the tail distribution of the probabilityof error, which extend the corresponding minimax lower bounds.

Solving two production scheduling problems with sequence-dependent set-up times

In today’s competitive markets, the importance of goodscheduling strategies in manufacturing companies lead to theneed of developing efficient methods to solve complexscheduling problems.In this paper, we studied two production scheduling problemswith sequence-dependent setups times. The setup times areone of the most common complications in scheduling problems,and are usually associated with cleaning operations andchanging tools and shapes in machines.The first problem considered is a single-machine schedulingwith release dates, sequence-dependent setup times anddelivery times. The performance measure is the maximumlateness.The second problem is a job-shop scheduling problem withsequence-dependent setup times where the objective is tominimize the makespan.We present several priority dispatching rules for bothproblems, followed by a study of their performance. Finally,conclusions and directions of future research are presented.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.