Understanding linear semi-infinite programming via linear programming over cones

作者：Zhang Qinghong^*

来源：Optimization, 2010, 59(8): 1247-1258.

DOI：10.1080/02331930903395865

• linear semi-infinite programming
• duality
• geometry of the feasible set
• optimality conditions

In this article, the standard primal and dual linear semi-infinite programming (DLSIP) problems are reformulated as linear programming (LP) problems over cones. Therefore, the dual formulation via the minimal cone approach, which results in zero duality gap for the primal-dual pair for LP problems over cones, can be applied to linear semi-infinite programming (LSIP) problems. Results on the geometry of the set of the feasible solutions for the primal LSIP problem and the optimality criteria for the DLSIP problem are also discussed.

• 出版日期2010