Abstract
In this paper, we establish a new non-homogeneous Farkas lemma for a linear semi-infinite inequality system, where the dual statement is given in terms of linear matrix inequalities and thus, it can be numerically verified by solving a semidefinite linear program. It is achieved by way of employing a special variable transformation together with a strong separation theorem. Consequently, we establish a duality theorem for a class of parametric linear semi-infinite programs which admit semi-definite linear programming (SDP) dual problems. A numerical example is given to show how a parametric linear semi-infinite optimization problem can be solved by way of solving its SDP dual problem using the Matlab toolbox CVX.
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