Two Types of Approximate Saddle Points

Abstract

In this paper, we study two types of approximate solutions for a vector optimization problem in Banach space setting. Our main concern is to define two new concepts of approximate saddle points and relate them to the above solution concepts. As a result, a dual is formulated, and duality results are established.

Keywords:

• Approximate quasi efficient solution
• Approximate quasi saddle point
• Approximate saddle point
• Vector Lagrangian
• Vector optimization

AMS Subject Classification:

• 90C46
• 49N15

ACKNOWLEDGMENTS

This work is dedicated to the late Professor M. C. Puri, IIT Delhi.

The authors wish to express deep gratitude to Prof. S. Chandra, IIT Delhi, for constant inspiration.