In a paper published in 1978, McEliece, Rodemich and Rumsey improved the Lovasz bound for the maximum clique problem. This strengthening has become well known under the name Lovasz-Schrijver bound and is usually denot...
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In a paper published in 1978, McEliece, Rodemich and Rumsey improved the Lovasz bound for the maximum clique problem. This strengthening has become well known under the name Lovasz-Schrijver bound and is usually denoted by '. This article now deals with situations where this bound is not exact. To provide instances for which the gap between this bound and the actual clique number can be arbitrarily large, we establish homomorphy results for this bound under cosums and products of graphs. In particular we show that for circulant graphs of prime order there must be a positive gap between the clique number and the bound.
This paper develops a semidefinite programming approach to computing bounds on the range of allowable absence of arbitrage prices for a European call option when option prices at other strikes and expirations are avai...
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This paper develops a semidefinite programming approach to computing bounds on the range of allowable absence of arbitrage prices for a European call option when option prices at other strikes and expirations are available and when moment related information on the underlying is known. The moment related information is incorporated in the problem through the fictitious prices of polynomial valued securities. The optimization then comes from relaxing a risk neutral pricing optimization problem in terms of moments of measures from a decomposition of the risk neutral pricing measure. We demonstrate this optimization formulation with computations using moment data from the standard Black-Scholes option pricing model and Merton's jump diffusion model.
By replacing the category of smooth vector bundles of finite rank over a manifold with the category of what we call smooth Euclidean fields, which is a proper enlargement of the former, and by considering smooth actio...
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By replacing the category of smooth vector bundles of finite rank over a manifold with the category of what we call smooth Euclidean fields, which is a proper enlargement of the former, and by considering smooth actions of Lie groupoids on smooth Euclidean fields, we are able to prove a Tannaka duality theorem for proper Lie groupoids. The notion of smooth Euclidean field we introduce here is the smooth, finite dimensional analogue of the usual notion of continuous Hilbert field. (C) 2009 Elsevier B.V. All rights reserved.
Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Clos...
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Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. A limiting form of these estimators constrains solutions to the class of quasi-concave densities.
In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing ...
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In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing edges is maximum. This problem has been introduced in (Galbiati and Maffioli, Theor Comput Sci 385 (2007), 78-87) where polynomial time randomized approximation algorithms are proposed and their performance guarantees are analyzed in the case of non-negative integer weights. In this article, we present extensive computational experience with these algorithms on a large number of different graphs. We then extend the analysis of these algorithms to integer weights not restricted in sign, and continue the computational testing. It turns out that the approximation ratios obtained are always substantially better than those guaranteed by the theoretical analysis. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 55(3), 247-255 2010
Analysis and safety considerations of chemical and biological processes require complete knowledge of the set of all feasible steady states. Nonlinearities, uncertain parameters, and discrete variables complicate the ...
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Analysis and safety considerations of chemical and biological processes require complete knowledge of the set of all feasible steady states. Nonlinearities, uncertain parameters, and discrete variables complicate the task of obtaining this set. In this paper, the problem of outer-approximating the region of feasible steady states, for processes described by uncertain nonlinear differential algebraic equations including discrete variables and discrete changes in the dynamics, is addressed. The calculation of the outer bounds is based on a relaxed version of the corresponding feasibility problem. It uses the Lagrange dual problem to obtain certificates for regions in state space not containing steady states. These infeasibility certificates can be computed efficiently by solving a semidefinite program, rendering the calculation of an outer bounding set computationally feasible. The derived method guarantees globally valid outer bounds for the feasible steady states. The method is exemplified by the analysis of a simple chemical reactor showing parametric uncertainties and large variability due to the appearance of bifurcations characterising the ignition and extinction of a reaction. (C) 2010 Elsevier Ltd. All rights reserved.
In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing ...
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In the Maximum Cut with Limited Unbalance problem, we want to partition the vertices of a weighted graph into two sets of sizes differing at most by a given threshold B, so that the sum of the weights of the crossing edges is maximum. This problem has been introduced in (Galbiati and Maffioli, Theor Comput Sci 385 (2007), 78-87) where polynomial time randomized approximation algorithms are proposed and their performance guarantees are analyzed in the case of non-negative integer weights. In this article, we present extensive computational experience with these algorithms on a large number of different graphs. We then extend the analysis of these algorithms to integer weights not restricted in sign, and continue the computational testing. It turns out that the approximation ratios obtained are always substantially better than those guaranteed by the theoretical analysis. (C) 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 55(3), 247-255 2010
We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the firs...
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ISBN:
(纸本)9781450302111
We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the first two moments of the service time and the interarrival time. The upper bounds on the tail distributions are integrated to obtain the upper bounds on the corresponding expectations. We also extend the formulation of the SDP, using the higher moments of the service time and the interarrival time, and calculate upper bounds and lower bounds numerically.
In this article, a detection strategy based on variable neighborhood search (VNS) and semidefinite relaxation of the multiuser model maximum likelihood (ML) is investigated. The VNS method provides a good method for s...
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In this article, a detection strategy based on variable neighborhood search (VNS) and semidefinite relaxation of the multiuser model maximum likelihood (ML) is investigated. The VNS method provides a good method for solving the ML problem while keeping the integer constraints. A SDP relaxation is used as an efficient way to generate an initial solution in a limited amount of time, in particular using early termination. The SDP resolution tool used is the spectral bundle method developed by Helmberg. We show that using VNS can result in a better error rate, but at a cost of calculation time. (C) 2009 Wiley Periodicals, Inc. NETWORKS, Vol. 55(3), 187-193 2010
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