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...

the paper presents unified analytical solution for combining high-frequency and low-frequency economic time-series by additive and proportional denton methods with parametrical dependence on the initial values of variable and indicator in evident form. this solution spans denton’s original and cholette’s advanced benchmarking initial conditions as the subcases. computational complexity of the o...

A non-overlapping domain decomposition algorithm is proposed to solve the linear system arising from mixed finite element approximation of incompressible Stokes equations. A continuous finite element space for the pressure is used. In the proposed algorithm, Lagrange multipliers are used to enforce continuity of the velocity component across the subdomain boundary. The continuity of the pressur...

In this paper, cross entropy method is used for solving dual Lagrange support vector machine (SVM). Cross entropy (CE) method is a new practical approach which is widely used in some applications such as combinatorial optimization, learning algorithm and simulation. Our approach refers to Kernel Adatron which is solving dual Lagrange SVM using gradient ascent method. Hereby, the cross entropy m...

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...

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....

The general ellipse packing problem is to find a non-overlapping arrangement of n ellipses with (in principle) arbitrary size and orientation parameters inside a given type of container set. Here we consider the general ellipse packing problem with respect to an optimized circle container with minimal radius. Following the review of selected topical literature, we introduce a new model formulat...

In this paper, He’s variational iteration method (VIM) is used to obtain approximate analytical solutions of the Abelian differential equation. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of problem. The method is capable of reducing the size of calculation...