Abstract. Let $X_1$ and $X_2$ be real Banach spaces. Let $K$ be a weakly compact subset in $X_2$, $A\colon X_1\to X_2$ be a closed linear map and $\phi $ be a bounded linear functional on $X_1$. We consider the following linear programming problem: $$\hbox{Maximize }\phi(x) \hbox{ subject to }Ax\in K.$$ Conditions under which explicit solutions to the above problem can be found are studied. The solutions are represented in terms of generalized inverses of $A$ and an optimal solution of a linear program in the dual space $X_2$. These results are then applied to linear programs with equality constraints and explicitly constrained feasible sets.
AMS Subject Classification
(1991): 46B, 90C
Keyword(s):
Banach spaces,
Linear programming problems,
generalised inverses,
explicit solutions
Received April 12, 1995 and in revised form December 13, 1995. (Registered under 6128/2009.)
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