Linear programming is one of the most important usages of operation research methods in real life, that includes of one objective function and one or several constraints which can be in the form of equality and inequality. Most of the problems in the real world are include of inconsistent and astute uncertainty, because of this reason we can’t obtain the optimal solution easily. In this paper, ...

Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.

Necessary and su cient conditions for the equality of ordinary least squares and generalized least squares estimators in the linear regression model with rst order spatial error processes are given

Linear dependence of two Hilbert space operators is expressed in terms of equality in modulus of certain sesquilinear and quadratic forms associated with the operators. The forms are based on generalized numerical ranges.

We derive the matrix that minimizes a quadratic criterion subject to linear equality constraints. Since we do not assume that the matrix of the quadratic form criterion is nonsingular, our optimization result is more general than those previously published. We make use of the extended result of this paper to (i) obtain the best linear unbiased estimate of the parameters in a linear regression w...

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 (...

We present several new techniques for linear arithmetic constraint solving. They are all based on the linear cube transformation, a method presented here, which allows us to efficiently determine whether a system of linear arithmetic constraints contains a hypercube of a given edge length. Our first findings based on this transformation are two sound tests that find integer solutions for linear...

In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data. By using an extension of Rohn’s result for the linear pro...

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