- On the sufficiency of finite support duals in semi-infinite linear programming Amitabh Basu(abasumath.ucdavis.edu) Kipp Martin(kmartinchicagobooth.edu) Christopher Ryan(chris.ryanchicagobooth.edu) Abstract: We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show the finite support (Haar) dual is equivalent to the algebraic Lagrangian dual of the linear program. This settles a question left open by Anderson and Nash~\cite{anderson-nash}. This result implies that if there is a duality gap between the primal linear program and its finite support dual, then this duality gap cannot be closed by considering the larger space of dual variables that define the algebraic Lagrangian dual. However, if the constraint space corresponds to certain subspaces of all real-valued sequences, there may be a strictly positive duality gap with the finite support dual, but a zero duality gap with the algebraic Lagrangian dual. Keywords: Semi-infinite linear programs, Langrangian duality Category 1: Infinite Dimensional Optimization (Semi-infinite Programming ) Citation: Download: [PDF]Entry Submitted: 04/13/2013Entry Accepted: 04/13/2013Entry Last Modified: 04/13/2013Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.