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Let X be a partially ordered real Banach space, a,b ∈ X with a ≤ b. Let ϕ be a bounded linear functional on X. We call X a Ben-Israel-Charnes space (or a B-C space) if the linear program defined by Maximize ϕ(x) subject to a ≤ x ≤ b has an optimal solution for any ϕ, a and b. Such problems arise naturally in solving a class of problems known as Interval Linear Programs. B-C spaces were introduced in the author's doctoral thesis and were subsequently studied in [8] and [9]. In this article, we review...
2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary
optimality condition for an optimization problem which arise naturally from
a class of wide studied problems. In the second result we establish a sufficient
condition for the metric regularity of a set-valued map without continuity
assumptions.
This article introduces an algorithm for implicit High Dimensional Model Representation (HDMR) of the Bellman equation. This approximation technique reduces memory demands of the algorithm considerably. Moreover, we show that HDMR enables fast approximate minimization which is essential for evaluation of the Bellman function. In each time step, the problem of parametrized HDMR minimization is relaxed into trust region problems, all sharing the same matrix. Finding its eigenvalue decomposition, we...
This paper considers a distribution inventory system that consists of a single warehouse and several retailers. Customer demand arrives at the retailers according to a continuous-time renewal process. Material flow between echelons is driven by reorder point/order quantity inventory control policies. Our objective in this setting is to calculate the long-run inventory, backorder and customer service levels. The challenge in this system is to characterize the demand arrival process at the warehouse....
Given a weighted undirected graph G = (V,E),
a tree (respectively tour) cover of an edge-weighted graph is a set of edges which forms a tree (resp. closed walk) and covers every
other edge in the graph. The tree (resp. tour) cover problem is of finding a minimum weight tree (resp. tour) cover of G.
Arkin, Halldórsson and Hassin (1993) give approximation
algorithms with factors respectively 3.5 and 5.5. Later Könemann, Konjevod, Parekh, and Sinha (2003) study the
linear programming relaxations...
In this paper, a graph partitioning problem that arises in the design of SONET/SDH networks is defined and formalized. Approximation algorithms with performance guarantees are presented. To solve this problem efficiently in practice, fast greedy algorithms and a tabu-search method are proposed and analyzed by means of an experimental study.
In this paper, a graph partitioning problem that arises in the design of
SONET/SDH networks is defined and formalized. Approximation algorithms with
performance guarantees are presented. To solve this problem efficiently in
practice, fast greedy algorithms and a tabu-search method are proposed and
analyzed by means of an experimental study.
We consider a class of discrete-time Markov control processes with Borel state and action spaces, and -valued i.i.d. disturbances with unknown density Supposing possibly unbounded costs, we combine suitable density estimation methods of with approximation procedures of the optimal cost function, to show the existence of a sequence of minimizers converging to an optimal stationary policy
We consider the problem of approximating a probability measure defined on a metric space
by a measure supported on a finite number of points. More specifically we seek the
asymptotic behavior of the minimal Wasserstein distance to an approximation when the
number of points goes to infinity. The main result gives an equivalent when the space is a
Riemannian manifold and the approximated measure is absolutely continuous and compactly
supported.
We consider the problem of approximating a probability measure defined on a metric space by a measure supported on a finite number of points. More specifically we seek the asymptotic behavior of the minimal Wasserstein distance to an approximation when the number of points goes to infinity. The main result gives an equivalent when the space is a Riemannian manifold and the approximated measure is absolutely continuous and compactly supported.
We consider the problem of approximating a probability measure defined on a metric space
by a measure supported on a finite number of points. More specifically we seek the
asymptotic behavior of the minimal Wasserstein distance to an approximation when the
number of points goes to infinity. The main result gives an equivalent when the space is a
Riemannian manifold and the approximated measure is absolutely continuous and compactly
supported.
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