Perfect Duality in Solving Geometric Programming Problems Under Uncertainty

Abstract

We examine computational solutions to all of the geometric programming problems published in a recent paper in the Journal of Optimization Theory and Applications. We employed three implementations of published algorithms interchangeably to obtain "perfect duality" for all of these problems. Perfect duality is taken to mean that a computed solution of an optimization problem achieves two properties: (1) primal and dual feasibility and (2) equality of primal and dual objective function values, all within the accuracy of the machine employed. Perfect duality was introduced by Duffin (Math Program 4: [125][126][127][128][129][130][131][132][133][134][135][136][137][138][139][140][141][142][143]1973). When primal and dual objective values differ, we say there is a duality gap.