A generalized Farkas lemma with a numerical certificate and linear semi-infinite programs with SDP duals

作者：Chuong T D^*; Jeyakumar V

来源：Linear Algebra and Its Applications, 2017, 515: 38-52.

DOI：10.1016/j.laa.2016.11.008

• Linear semi-infinite
• Linear inequality constraints
• Farkas lemma
• Dual characterization

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.

• 出版日期2017-2-15