In this work we study convergence properties of sparse polynomial approximations for a class affine parametric saddle point problems, including the Stokes equations viscous incompressible flow, mixed formulation diffusion groundwater time-harmonic Maxwell electromagnetics, etc. Due to lack knowledge or intrinsic randomness, (viscosity, diffusivity, permeability, permittivity, etc.) coefficients...

Finding the global optimal solution for a general nonlinear program is a diicult task except for very small problems. In this paper we identify a class of non-linear programming problems called polynomial programming problems (PP). A polynomial program is an optimization problem with a scalar polynomial objective function and a set of polynomial constraints. By using Groebner Bases, we can dete...

Proof of the hypothesis Edmonds's, not polynomial of NPC-problems and classification of the problems with polynomial certificates Abstract We show that the affirmation P ⊆ N P (in computer science) erroneously and we prove the justice of the hypotesis J.Edmonds's P = N P. We show further that all the N P-complete problems is not polynomial and we give the classification of the problems with the...

we present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. numerical method of sixth-order with end conditions of the order 6 is derived. the convergence analysis of the method has been discussed. numerical examples are presented to illustra...

Based on reproducing kernel theory, an effective numerical technique is proposed for solving second order linear two-point boundary value problems with deviating argument. In this method, reproducing kernels with Chebyshev polynomial form are used (C-RKM). The convergence and an error estimation of the method are discussed. The efficiency and the accuracy of the method is demonstrated on some n...

This thesis addresses the kernelization properties of generic problems, defined via syntactical restrictions or by a problem framework. Polynomial kernelization is a formalization of data reduction, aimed at combinatorially hard problems, which allows a rigorous study of this important and fundamental concept. The thesis is organized into two main parts. In the first part we prove that all prob...

Polynomial optimization encompasses a very rich class of problems in which both the objective and constraints can be written in terms of polynomials on the decision variables. There is a well established body of research on quadratic polynomial optimization problems based on reformulations of the original problem as a conic program over the cone of completely positive matrices, or its conic dua...