Saddle points and duality in generalized geometric programming

Saddle Points and Pareto Points in Multiple Objective Programming

In this paper relationships between Pareto points and saddle points in multiple objective programming are investigated. Convex and nonconvex problems are considered and the equivalence between Pareto points and saddle points is proved in both cases. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. Partitions of the ind...

Geometric Duality and Linear Programming

Linear programs are problems that involve the optimization of a linear objective function subject to linear constraints. Every linear program has an inherent geometric representation. Each constraint defines an halfspace and the feasible region of the the linear program is the convex polyhedron defined by intersection of all the halfspaces. The maximal solution to the linear program (if it exis...

Geometric Duality in Multiple Objective Linear Programming

We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.

Subgradient Optimization, Generalized Programming, and Nonconvex Duality

Duality in generalized linear fractional programming

This is a generalization of a fractional programming problem (p = 1) which has been investigated quite actively in the last two decades [21 ]. In [20] many of the results in fractional programming are reviewed and extended. An extensive bibliography is given in [22]. An early application of generalized fractional programming (p > 1) is von Neumann's model of an expanding economy [25]. Here the ...