In this note, we revisit the classical first order necessary condition in mathematical programming in infinite dimension. The constraint set being defined by C = g−1(K) where g is a smooth map between Banach spaces, and K a closed convex cone, we show that existence of Lagrange-Karush-Kuhn-Tucker multipliers is equivalent to metric subregularity of the multifunction defining the constraint, and...

This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required use appropriate technique determine multipliers in that leads finding optimal solution problem. Our analysis aims find a suitable generate multipliers, and later these are used Multiobjective We propose search-based Lagrange multipliers. In our paper, we choose well-known s...

In hep-th/0312098 it was argued that by extending the “a-maximization” of hepth/0304128 away from fixed points of the renormalization group, one can compute the anomalous dimensions of chiral superfields along the flow, and obtain a better understanding of the irreversibility of RG flow in four dimensional supersymmetric field theory. According to this proposal, the role of the running coupling...