Search results for "Mathematical optimization"
showing 10 items of 1300 documents
Multiobjective GRASP with Path Relinking
2015
In this paper we review and propose different adaptations of the GRASP metaheuristic to solve multiobjective combinatorial optimization problems. In particular, we describe several alternatives to specialize the construction and improvement components of GRASP when two or more objectives are considered. GRASP has been successfully coupled with Path Relinking for single-objective optimization. Moreover, we propose different hybridizations of GRASP and Path Relinking for multiobjective optimization. We apply the proposed GRASP with Path Relinking variants to two combinatorial optimization problems, the biobjective orienteering problem and the biobjective path dissimilarity problem. We report …
Mean Field Linear Quadratic Games with Set Up Costs
2013
This paper studies linear quadratic games with set up costs monotonic on the number of active players, namely, players whose action is non-null. Such games arise naturally in joint replenishment inventory systems. Building upon a preliminary analysis of the properties of the best response strategies and Nash equilibria for the given game, the main contribution is the study of the same game under large population. We also analyze the influence of an additional disturbance in the spirit of the literature on H∞ control. Numerical illustrations are provided. © 2012 Springer Science+Business Media New York.
Introspection and equilibrium selection in 2 � 2 matrix games
1994
Game theory lacks an explanation of how players' beliefs are formed and why they are in equilibrium. This is the reason why it has failed to make significant advances with the problem of equilibrium selection even for quite siniple games, as 2x2 games with two strict Nash equilibria. Our paper models the introspection process by which the selected equilibrium is achieved in this class of games. Players begin their analysis with imprecise priors, obtained under weak restrictions formulated as Axioms. For a large class of reasoning dynamics we obtain as the solution the risk dominant Nash equilibrium.
Distributed Consensus for Discrete-Time Directed Networks of Multiagents with Time-Delays and Random Communication Links
2013
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/158731 Open Access This paper is concerned with the leader-following consensus problem in mean-square for a class of discrete-time multiagent systems. The multiagent systems under consideration are the directed and contain arbitrary discrete time-delays. The communication links are assumed to be time-varying and stochastic. It is also assumed that some agents in the network are well informed and act as leaders, and the others are followers. By introducing novel Lyapunov functionals and employing some new analytical techniques, sufficient conditi…
Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam
2014
The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a …
Influence of the evolutionary optimization parameters on the optimal topology
2016
Topological optimization can be considered as one of the most general types of structural optimization. Between all known topological optimization techniques, the Evolutionary Structural Optimization represents one of the most efficient and easy to implement approaches. Evolutionary topological optimization is based on a heuristic general principle which states that, by gradually removing portions of inefficient material from an assigned domain, the resulting structure will evolve towards an optimal configuration. Usually, the initial continuum domain is divided into finite elements that may or may not be removed according to the chosen efficiency criteria and other parameters like the spee…
Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations
2008
In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of…
Optimal Hedging of Option Portfolios with Transaction Costs
2006
One of the most successful approaches to option hedging with transaction costs is the utility based approach pioneered by Hodges and Neuberger (1989). However, this approach has one major drawback that prevents the broad application of this approach in practice: the lack of a closed-form solution. The direct numerical computations of the utility based hedging strategy are cumbersome in a practical implementation. Despite some recent advances in finding an explicit description of the utility based hedging strategy by using either asymptotic, approximation, or other methods, so far they were concerned primarily with hedging a single plain-vanilla option. However, in practice one often faces t…
Optimal Index Tracking Under Transaction Costs and Impulse Control
1998
We apply impulse control techniques to a cash management problem within a mean-variance framework. We consider the strategy of an investor who is trying to minimise both fixed and proportional transaction costs, whilst minimising the tracking error with respect to an index portfolio. The cash weight is constantly fluctuating due to the stochastic inflow and outflow of dividends and liabilities. We show the existence of an optimal strategy and compute it numerically.
Towards efficient inductive synthesis: Rapid construction of local regularities
2006
Given several input/output examples of some function we can state the problem: what is the “simplest” function which complies with these examples. This problem is well studied and is known to be very hard in the general case. In this paper we address a special case of the problem, when the target function can be expressed as a simple composition of known functions. We propose a new inductive synthesis algorithm for this case and show that it is efficient enough to synthesize complex geometry formulas.