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...

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...

We propose a systematic method of dealing with the canonical constrained structure of reducible systems in the Dirac and symplectic approaches which involves an enlargement of phase and configuration spaces, respectively. It is not necessary, as in the Dirac approach, to isolate the independent subset of constraints or to introduce , as in the symplectic analysis, a series of lagrange multiplie...

We consider the coupling of compressible and nearly incompressible materials within the framework of mortar methods. Taking into account the locking effect, we use a suitable discretization for the nearly incompressible material and work with a standard conforming discretization elsewhere. The coupling of different discretization schemes in different subdomains are handled by flexible mortar te...

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem.We tackle the problem using duality concept, differently from traditional approaches. Ourmethod is based on Lagrangian relaxation. Lagrangemultipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the cap...

We study the five-dimensional supergravity dual of the a-maximization under AdS5/CFT4 duality. We firstly show that the a-maximization is mapped to the attractor equation in five-dimensional gauged supergravity, and that the trial a-function is the inverse cube of the superpotential of the five-dimensional theory. There is also a version of a-maximization in which one extremizes over Lagrange m...

We present well-known interpretations of Lagrange multipliers in physical and economic applications, and introduce a new interpretation in nonlinear pricing problem. The multipliers can be interpreted as a network of directed flows between the buyer types. The structure of the digraph and the fact that the multipliers usually have distinctive values can be used in solving the optimization probl...