On the determination of first feasible - near optimal solutions of linear programming problems using the projected gradient

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1975

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Abstract

Given the direct linear programming problem (D.L.P.P.) Maximize (x,c) where Ax = b , x e we are interested in the following questions : How much information regarding the nature of an optimal solution to the D.I.P.P. can be obtained from any one of the vectors c , (I - A+A)c or A+b ? Can enough information be obtained from c , (I - A+A)c or A+b so as to provide a means of determining first feasible - near optimal solutions ? This study describes numerical experiments designed to shed light on the answer to the first question formulated. Results of the experiments are presented and discussed. A proposal for future research along this line of development is also given.

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