Multipliers and general Lagrangians

Abstract

We combine a Lagrangian approach inspired by convex and quasiconvex dualities with a penalization approach to mathematical programming. We use the ideas of abstract convexity. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as elements of generalized subdifferentials of the performance function associated with a dualizing parameterization of the given problem.

Keywords:

• Dualizing parameterization
• Lagrangian
• Mathematical programming
• Multiplier
• Penalization
• Performance function

Notes

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.

Additional information

Notes on contributors

Alexander M. Rubinov

Dedicated to V.F. Demyanov on the occasion of his 65th birthday.