where x, c, c ∈ R1 , x, c, c ∈ R2 , b ∈ R, A1 is an m × n1 matrix, A2 is an m × n2 matrix, and T denotes the transposition. Such problems may arise when there are two decision makers at different hierarchical levels having joint constraints and different and possibly conflicting objectives. The decision-making process is sequential. The leader controlling the variables of x has the first choice...

Recently, Y.Q. Bai, M. El Ghami and C. Roos [3] introduced a new class of so-called eligible kernel functions which are defined by some simple conditions. The authors designed primal-dual interiorpoint methods for linear optimization (LO) based on eligible kernel functions and simplified the analysis of these methods considerably. In this paper we consider the semidefinite optimization (SDO) pr...

In [] we defined Inf-Datalog and characterized the fragments of Monadic inf-Datalog that have the same expressive power as Modal Logic (resp. CTL, alternation-free Modal μ-calculus and Modal μ-calculus). We study here the time and space complexity of evaluation of Monadic inf-Datalog programs on finite models. We deduce a new unified proof that model checking has 1. linear data and program comp...

In this paper, we analyze the convergence of the Alternating Direction Method of Multipliers (ADMM) as a matrix recurrence for the particular case of a quadratic program or a linear program. We identify a particular combination of the vector iterates in the standard ADMM iteration that exhibits almost monotonic convergence. We present an analysis which indicates the convergence depends on the e...

In this short report, we analyze the convergence of ADMM as a matrix recurrence for the particular case of a quadratic program or a linear program. We identify a particular combination of the vector iterates in the standard ADMM iteration that exhibits monotonic convergence. We present an analysis which indicates the convergence depends on the eigenvalues of a particular matrix operator. The th...

For any linear program, we show that a slight random relative perturbation of that linear program has small condition number with high probability. Following [ST01], we call this smoothed analysis of the condition number. Part of our main result is that the expectation of the log of the condition number of any appropriately scaled linear program subject to a Gaussian perturbation of variance σ ...

OWEN (1975) introduced linear production (LP) situations and TIMMER, BORM and SUIJS (1998) introduced more general situations involving the linear transformation of products (LTP). They showed that the corresponding LTP games are totally balanced. In this paper we look at LTP situations with an infinite number of transformation techniques. The linear program that calculates the maximal profit, ...

We study the problem of preemptive scheduling of n equal-length jobs with given release times on m identical parallel machines. The objective is to minimize the average flow time. Recently, Brucker and Kravchenko [1] proved that the optimal schedule can be computed in polynomial time by solving a linear program with O(n) variables and constraints, followed by some substantial post-processing (w...

We consider the problem of transformations of logic pro grams without function symbols database logic programs into a special subclass namely linear logic programs Linear logic programs are de ned to be the programs whose rules have at most one intentional atom in their bodies a We investigate linearizability of several syntactically de ned subclasses of programs and present both positive and n...

In this paper we derive and exploit duality in general two-stage adaptive linear optimization models. The equivalent dualized formulation we derive is again a two-stage adaptive linear optimization model. Therefore, all existing solution approaches for two-stage adaptive models can be used to solve or approximate the dual formulation. The new dualized model differs from the primal formulation i...