Duality Via Halfspaces (Five Steps to Duality)

This note shows that half spaces play a very special role in the development of duality. In addition to the minimum norm duality, the duality in linear programming, and Wolfe's and Johri's formulations in nonlinear programming can all be derived via half spaces by following an identical five step. ( Absract for ORSA conference) The minimum norm duality in optimization theory and the duality in linear programming are different concepts applied to different problems. This talk shows that the same five steps can be used to derive both dualities directly from their primal problems.