A rule to assign physical meaning to Lagrange multipliers is discussed. Examples from mechanics, statistical mechanics and quantum mechanics are given.

A Lagrange multiplier and Hopfield-type barrier function method is proposed for approximating a solution of the traveling salesman problem. The method is derived from applications of Lagrange multipliers and a Hopfield-type barrier function and attempts to produce a solution of high quality by generating a minimum point of a barrier problem for a sequence of descending values of the barrier par...

The Support Vector Machine (SVM) idea has attracted recent attention in solving classiication and regression problems. As an example based method, SVMs distinguish two point classes by nding a separating boundary layer, which is determined by points that become known as Support Vectors (SVs). While the computation of the separating boundary layer is formulated as a linearly constrained Quadrati...

We study homological invariants of smooth families of real quadratic forms as a step towards a “ Lagrange multipliers rule in the large” that intends to describe topology of smooth vector functions in terms of scalar Lagrange functions.

In the new restructured electricity power industry, a Generation Company (GENCO) with thermo-electric amenities faces the optimal problem of how to attain a maximum profit by considering the price uncertainties. In deregulated power markets, the maximization of profit is different from the minimization of cost because generation companies no longer have the obligation to serve the whole demand....

A higher-order discontinuous enrichment method (DEM) with Lagrange multipliers is proposed for the efficient finite element solution on unstructured meshes of the advection-diffusion equation in the high Péclet number regime. Following the basic DEM methodology, the usual Galerkin polynomial approximation is enriched with free-space solutions of the governing homogeneous partial differential eq...

Mikhail A. Bragin • Peter B. Luh • Joseph H. Yan • Nanpeng Yu • Gary A. Stern Communicated by Fabián Flores-Bazàn Abstract Studies have shown that the surrogate subgradient method, to optimize non-smooth dual functions within the Lagrangian relaxation framework, can lead to significant computational improvements as compared to the subgradient method. The key idea is to obtain surrogate subgradi...