A discontinuous Galerkin type nonconforming element method and a local flux matching nonconforming element method for the second order elliptic boundary value problems are presented. Both of these methods enjoy the local flux conservation property. The local flux matching method finds a numerical solution in the same solution space of the DG type nonconforming element method, but it achieves mu...

Minimization with orthogonality constraints (e.g., X>X = I) and/or spherical constraints (e.g., ‖x‖2 = 1) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive t...

By means of a highly accurate, multi-domain, pseudo-spectral method, we investigate the solution space of uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies. It turns out that this space can be divided up into classes of solutions. In this paper, we present two new classes including relativistic core-ring and tworing solutions. Combining our knowledge of the first four c...

An iteration of the sequential quadratically constrained quadratic programming method (SQCQP) consists of minimizing a quadratic approximation of the objective function subject to quadratic approximation of the constraints, followed by a linesearch in the obtained direction. Methods of this class are receiving attention due to the development of efficient interior point techniques for solving s...

In managerial and economic applications, there appear problems in which the goal is to simultaneously optimize several criteria functions (CFs). However, since the CFs are in conflict with each other in such cases, there is not a feasible point available at which all CFs could be optimized simultaneously. Thus, in such cases, a set of points, referred to as 'non-dominate' points (NDPs), will be...