The paper deals with the economic dispatch problem for a district heating system. The distribution network is modeled with a number of nodes and arcs, implying that time delays and restrictions in distribution capacity can be considered. A solution algorithm for the corresponding nonlinear optimization problem is proposed. The method is based on Lagrangian relaxation and exploits the relations ...

It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian relaxation. It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal s...

The purpose of this paper is to consider the set-valued optimization problem in Asplund spaces without convexity assumption. By a scalarization function introduced by Tammer and Weidner (J Optim Theory Appl 67:297–320, 1990), we obtain the Lagrangian condition for approximate solutions on set-valued optimization problems in terms of the Mordukhovich coderivative.

It is known that in convex optimization, the Lagrangian associated with a constrained problem is usually a saddle function, which leads to the classical saddle Lagrange duality (i. e. the monoduality) theory. In nonconvex optimization, a so-called superLagrangian was introduced in [1], which leads to a nice biduality theory in convex Hamiltonian systems and in the so-called d.c. programming.

Starting from a reformulation of Cramer & Singer Multiclass Kernel Machine, we propose a Sequential Minimal Optimization (SMO) like algorithm for incremental and fast optimization of the lagrangian. The proposed formulation allowed us to de ne very e ective new pattern selection strategies which lead to better empirical results.