10,515 research outputs found
Discrete optimization problems with random cost elements
In a general class of discrete optimization problems, some of the elements mayhave random costs associated with them. In such a situation, the notion of optimalityneeds to be suitably modified. In this work we define an optimal solutionto be a feasible solution with the minimum risk. We focus on the minsumobjective function, for which we prove that knowledge of the mean values ofthese random costs is enough to reduce the problem into one with fixed costs.We discuss the implications of using sample means when the true means ofthe costs of the random elements are not known, and explore the relation betweenour results and those from post-optimality analysis. We also show thatdiscrete optimization problems with min-max objective functions depend moreintricately on the distributions of the random costs.
On solving discrete optimization problems with one random element under general regret functions
In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and define an optimal solution as one having the least possible risk. We show that for discrete optimization problems with one random element and with min-sum objective functions a least risk solution for the stochastic problem can be obtained by solving a non-stochastic counterpart where the latter is constructed by replacing the random element of the former with a suitable parameter. We show that the above surrogate is the mean if the stochastic problem has only one symmetrically distributed random element. We obtain bounds for this parameter for certain classes of asymmetric distributions and study the limiting behavior of this parameter in details under two asymptotic frameworks. \u
On solving discrete optimization problems with multiple random elements under general regret functions
In this paper we attempt to find least risk solutions for stochastic discrete optimization problems (SDOP) with multiple random elements, where the feasibility of a solution does not depend on the particular values the random elements in the problem take. While the optimal solution, for a linear regret function, can be obtained by solving an auxiliary (non-stochastic) discrete optimization problem (DOP), the situation is complex under general regret. We characterize a finite number of solutions which will include the optimal solution. We establish through various examples that the results from Ghosh, Mandal and Das (2005) can be extended only partially for SDOPs with additional characteristics. We present a result where in selected cases, a complex SDOP may be decomposed into simpler ones facilitating the job of finding an optimal solution to the complex problem. We also propose numerical local search algorithms for obtaining an optimal solution. \u
High frequency quasi-normal modes for black holes with generic singularities II: Asymptotically non-flat spacetimes
The possibility that the asymptotic quasi-normal mode (QNM) frequencies can
be used to obtain the Bekenstein-Hawking entropy for the Schwarzschild black
hole -- commonly referred to as Hod's conjecture -- has received considerable
attention. To test this conjecture, using monodromy technique, attempts have
been made to analytically compute the asymptotic frequencies for a large class
of black hole spacetimes. In an earlier work, two of the current authors
computed the high frequency QNMs for scalar perturbations of
dimensional spherically symmetric, asymptotically flat, single horizon
spacetimes with generic power-law singularities. In this work, we extend these
results to asymptotically non-flat spacetimes. Unlike the earlier analyses, we
treat asymptotically flat and de Sitter spacetimes in a unified manner, while
the asymptotic anti-de Sitter spacetimes is considered separately. We obtain
master equations for the asymptotic QNM frequency for all the three cases. We
show that for all the three cases, the real part of the asymptotic QNM
frequency -- in general -- is not proportional to ln(3) thus indicating that
the Hod's conjecture may be restrictive.Comment: 16 pages; 3 Figures; Revtex4; Final Version -- To appear in CQ
Discrete optimization problems with random cost elements
In a general class of discrete optimization problems, some of the elements mayhave random costs associated with them. In such a situation, the notion of optimalityneeds to be suitably modified. In this work we define an optimal solutionto be a feasible solution with the minimum risk. We focus on the minsumobjective function, for which we prove that knowledge of the mean values ofthese random costs is enough to reduce the problem into one with fixed costs.We discuss the implications of using sample means when the true means ofthe costs of the random elements are not known, and explore the relation betweenour results and those from post-optimality analysis. We also show thatdiscrete optimization problems with min-max objective functions depend moreintricately on the distributions of the random costs
- …