In this letter, we investigate the problem of actuator scheduling for networked control systems. Given a stochastic linear system with number actuators, consider case that one is activated at each time. This combinatorial in nature and NP-Hard to solve. We propose convex relaxation problem, use relaxed solution as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3...

1. Recently Waldmann pointed out that linear transport relaxation equations can be derived from a variational principle, if certain time reversal symmetries hold [1]. He postulated an action with a quadratic Lagrangian, which implies by its extremum the relaxation equations as its EulerLagrange equations. In the following i) the relation of Waldmann's action to the Onsager-Machlup [2] theory is...

Mixed-Integer Programs (MIP’s) involving logical implications modelled through big-M coefficients, are notoriously among the hardest to solve. In this paper we propose and analyze computationally an automatic problem reformulation of quite general applicability, aimed at removing the model dependency on the big-M coefficients. Our solution scheme defines a master Integer Linear Problem (ILP) wi...

ABSTRACT We tackle the problem of designing revenue maximizing auctions in the Bayesian framework, when bidders not only have private valuations but also private budgets. We consider the setting of selling divisible goods to multiple agents each with linear utilities, but agents cannot pay beyond their budget. We focus on the case when the auctioneer can check that bidders do not over-report th...

In 2004 Newman [43] suggested a semidefinite programming relaxation for the Linear Ordering Problem (LOP) that is related to the semidefinite program used in the Goemans-Williamson algorithm to approximate the Max Cut problem [22]. Her model is based on the observation that linear orderings can be fully described by a series of cuts. Newman [43] shows that her relaxation seems better suited for...

The concept of a relaxation spectrum is used to compute the absorption and dispersion of a linear anelastic solid. The Boltzmann aftereffect equation is solved for a solid having a linear relationship between stress and strain and their first time derivatives, the 'standard linear solid', and having a distribution of relaxation times. The distribution function is chosen to give a nearly constan...

Let G be a simple undirected graph with node set V (G) and edge set E(G). We call a subset F ⊆ E(G) independent if F is contained in the edge set of a complete multipartite (not necessarily induced) subgraph of G, F is dependent otherwise. In this paper we characterize the independents and the minimal dependents of G. We note that every minimal dependent of G has size two if and only if G is fa...

We investigate dynamic policies for allocating scarce inventory to stochastic demand for multiple fare classes, in a network environment so as to maximize total expected revenues. Typical applications include sequential reservations for an airline network, hotel, or car rental service. We propose and analyze a new algorithm based on approximate dynamic programming, both theoretically and comput...

Although the lift-and-project operators of Lovász and Schrijver have been the subject of intense study, their M(K , K ) operator has received little attention. We consider an application of this operator to the stable set problem. We begin with an initial linear programming (LP) relaxation consisting of clique and non-negativity inequalities, and then apply the operator to obtain a stronger ext...

In this work we focus on solving quadratically constrained pseudoboolean optimization problems with quadratic objective as mixed integer linear programs. The standard mixed integer linear formulation of such problems is strengthened using valid inequalities derived from solving Reformulation-Linearization relaxation called partial DRL* relaxation. The proposed PDRL* relaxation features block-de...