SUMMARY In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain sho...

This paper proposes a new method based on the ideal input vector to estimate inputs of a given decision making unit (DMU) when some or all of its outputs are increased to maintain its current efficiency level. In other words, this paper studied the following question: How much would be the increase in the inputs of the DMU if the decision maker increases certain outputs to a particular unit in ...

To illustrate this technique, we give an alternate proof that the natural linear program for bipartite perfect matching is integral. Then we study the classical minimum spanning tree problem, and see how to attack this problem using linear programming. In fact, an exponential size LP will be used for the minimum spanning tree problem. First we will show how to solve this exponential size LP via...

A class of simplex methods for solving linear programming (LP) problems, with cosine pivot rule, have been presented in some recent papers. In this paper we show that the cosine rule used in this class is equivalent to the mostobtuse-angle pivot rule, proposed by Pan (1990). The relation between the direct method for LP and the most-obtuse-angle rule is discussed.

We present an implementation of the LPDual Active Set Algorithm (LP DASA) based on a quadratic proximal approximation, a strategy for dropping inactive equations from the constraints, and recently developed algorithms for updating a sparse Cholesky factorization after a low-rank change. Although our main focus is linear programming, the first and second-order proximal techniques that we develop...

A recent article in this journal by E. Chuvieco demonstrated the potential of integrating optimization methods (speci® cally, linear programming) with geographical information systems (GIS) through the use of a small example in land-use planning. The bene® ts attainable from the combined use of these technologies are, in our opinion, beyond question. However, several misconceptions regarding th...

Linear programming (LP) is a widely used tool in management decision making. Theoretically, sensitivity analysis of LP problems provides useful information for the decision maker. In practice, however, most LP software provides misleading sensitivity information if the optimal solution is degenerate. The paper shows how sensitivity analysis of LP problems can be done correctly when the optimal ...

We give a link to a page on the Web on which we deposited a set of eight huge Linear Programming (LP) problems for IntensityModulated Proton Therapy (IMPT) treatment planning. These huge LP problems were employed in our recent research and we were asked to make them public.

In this paper, a new method is proposed to find the fuzzy optimal solution of fully fuzzy linear programming (abbreviated to FFLP) problems. Also, we employ linear programming (LP) with equality constraints to find a non-negative fuzzy number vector x̃ which satisfies Ãx̃ = b̃, where à is a fuzzy number matrix. Then we investigate the existence of a positive solution of fully fuzzy linear system (...

In this paper, we propose fuzzy linear programming support vector machines (LP-SVMs) that resolve unclassifiable regions for multiclass problems. Namely, in the directions orthogonal to the decision functions obtained by training the LP-SVM, we define membership functions. Then by the minimum or average operation for these membership functions we define a membership function for each class. We ...