It is crucial to maximize marketing efficiency and customer satisfaction in personalized marketing. In this paper, we raise the multiple recommendation problem which occurs when performing several personalized campaigns simultaneously. We formulate the multi-campaign assignment problem to solve this issue and propose methods for solving the problem. The most notable element is the Lagrange mult...

In modern DSL systems, multi-user crosstalk is the major source of performance degradation. Optimal Spectrum Balancing (OSB) is a centralized algorithm that optimally allocates the available transmit power over frequencies, thereby mitigating the effect of crosstalk. OSB uses Lagrange multipliers to enforce constraints that are coupled over frequencies. However, finding the optimal Lagrange mul...

In modern DSL systems, multi-user crosstalk is a major source of performance degradation. Optimal Spectrum Balancing (OSB) is a centralized algorithm that mitigates the effect of crosstalk by allocating optimal transmit spectra to all interfering DSL modems. By the use of Lagrange multipliers the algorithm decouples the spectrum management problem into per-tone optimization problems. The remain...

Variational problems under uniform quasiconvex constraints on the gradient are studied. Our technique consists in approximating the original problem by a one−parameter family of smooth unconstrained optimization problems. Existence of solutions to the problems under consideration is proved as well as existence of lagrange multipliers associated to the uniform constraint; no constraint qualifica...

Lagrange multipliers for distributed parameter systems with mixed control-state constraints may exhibit better regularity properties than those for problems with pure pointwise state constraints, (1), (2), (4). Under natural assumptions, they are functions of certain L-spaces, while Lagrange multpliers for pointwise state constraints are, in general, measures. Following an approach suggested in...

Lagrange multipliers are present in any gauge theory. They possess peculiar gauge transformation which is not generated by the constraints in the model as it is the case with the other variables. For rank one gauge theories we show how to alter the constraints so that they become generators of the local symmetry algebra in the space of Lagrange multipliers too. We also discuss the limitations o...

A large class of optimization problems can be modeled as minimization of an objective function subject to constraints given in a form of set inclusions. We discuss in this paper augmented Lagrangian duality for such optimization problems. We formulate the augmented Lagrangian dual problems and study conditions ensuring existence of the corresponding augmented Lagrange multipliers. We also discu...

Recently, we have proposed the discrete Lagrange-multiplier method (DLM) to solve satissability problems. Instead of restarting from a new starting point when the search reaches a local minimum in the objective space, the Lagrange multipliers of violated constraints in DLM provide a force to lead the search out of the local minimum and move it in a direction provided by the multipliers. In this...

In this paper, a new approach to the variational iteration method is introduced to solve systems of first-order differential equations. Since higher-order differential equations can almost always be converted into a first-order system of equations, the proposed method is still applicable to a wide range of differential equations. This generalised approach, unlike the classical method, uses rest...