Showing papers on "Solution set published in 1973"

An Algorithm for Solving Multicriterion Linear Programming Problems with Examples

Abstract: The purpose of this paper is to develop a useful technique for solving linear programmes involving more than one objective function. Motivation for solving multicriterion linear programmes is given along with the inherent difficulty associated with obtaining a satisfactory solution set. By applying a linear programming approach for the solution of two person–zero sum games with mixed strategies, it is shown that a linear optimization problem with multiple objective functions can be formulated in this fashion in order to obtain a solution set satisfying all the requirements for an efficient solution of the problem. The solution method is then refined to take into account disparities between the magnitude of the values generated by each of the objective functions and solution preferences as determined by a decision-maker. A summary of the technique is then given along with several examples in order to demonstrate its applicability.

Generic properties of the complementarity problem

Abstract: Givenf: R+n→ Rn, the complementarity problem is to find a solution tox ≥ 0,f(x) ≥ 0, and 〈x, f(x)〉 = 0. Under the condition thatf is continuously differentiable, we prove that for a generic set of such anf, the problem has a discrete solution set. Also, under a set of generic nondegeneracy conditions and a condition that implies existence, we prove that the problem has an odd number of solutions.

Solution Sets of Convex Programs Related to Chemical Equilibrium Problems

Abstract: We consider the program I infFx, subject to x ∈ H and Ax = b, where H is any convex set in the positive orthant, A is any m × n matrix, b is any m-vector, and F is convex and continuous on H. A subsidiary program is used to study the nature of the constraint set and optimal solution set of program I. The method used involves classifying duality states of the program with respect to duality states of its subsidiary program. Extensions are thereby obtained of Bigelow-DeHaven-Shapiro results [SIAM J. Appl. Math. 18, 768-775 1970] on the set of solutions to chemical equilibrium problems. An example of Bigelow and Shapiro is given illustrating the states by means of a simple, ideal, one-phase chemical-equilibrium problem in two dimensions.

Strengthened theorems for set stability of differential equations

Abstract: Set stability and uniform set stability involve known specific bounds on the solutions of differential equations. A result m set theory is employed in strengthening previously developed Liapunov-liko theorems for these forms of stability. An example illustrating the advantages of the new theorems is presented.