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Lexicographic α-robustness: an application to the 1-median problem

R. Kalaï, M. A. Aloulou, Ph. Vallin, D. Vanderpooten (2010)

RAIRO - Operations Research

In the last decade, several robustness approaches have been developed to deal with uncertainty. In decision problems, and particularly in location problems, the most used robustness approach rely either on maximal cost or on maximal regret criteria. However, it is well known that these criteria are too conservative. In this paper, we present a new robustness approach, called lexicographic α-robustness, which compensates for the drawbacks of criteria based on the worst case. We apply this approach...

LFS functions in multi-objective programming

Luka Neralić, Sanjo Zlobec (1996)

Applications of Mathematics

We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction, where...

Limited memory solution of bound constrained convex quadratic problems arising in video games

Michael C. Ferris, Andrew J. Wathen, Paul Armand (2007)

RAIRO - Operations Research

We describe the solution of a bound constrained convex quadratic problem with limited memory resources. The problem arises from physical simulations occurring within video games. The motivating problem is outlined, along with a simple interior point approach for its solution. Various linear algebra issues arising in the implementation are explored, including preconditioning, ordering and a number of ways of solving an equivalent augmented system. Alternative approaches are briefly surveyed, ...

Limited space double channel Markovian queue with heterogeneus servers.

O.P. Sharma, J. Dass (1990)

Trabajos de Investigación Operativa

For a double channel Markovian queue with finite waiting space and unequal service rates at the two counters, the difference equations satisfied by the Laplace transforms of the state probabilities at finite time are solved and the state probabilities have been obtained. The closed form of the state probabilities can be used to obtain the important parameters of the system.

Limiting average cost control problems in a class of discrete-time stochastic systems

Nadine Hilgert, Onesimo Hernández-Lerma (2001)

Applicationes Mathematicae

We consider a class of d -valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation x t + 1 = G ( x t , a t ) + ξ t (t = 0,1,... ), for each fixed n = 0,1,..., where the ξ t are i.i.d. random vectors, and the Gₙ are given functions converging pointwise to some function G as n → ∞. Under suitable hypotheses, our main results state the existence of stationary control policies that are expected average cost (EAC) optimal and sample path average cost (SPAC) optimal for...

Linear complementarity problems and bi-linear games

Gokulraj Sengodan, Chandrashekaran Arumugasamy (2020)

Applications of Mathematics

In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of 𝐙 -transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of 𝐙 -transformations....

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