In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

in this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual interior point method (ipm) based on a new kernel function with a trigonometric barrier term. iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. although our proposed kernel function is neither a self-regular (sr) function nor logarithmic barrier ...

We introduce a new barrier function which has a linear growth term in its kernel function. So far all existing kernel functions have a quadratic (or higher degree) growth term. Despite this, a large-update primal-dual interior-point method based on this kernel function has the same iteration bound as the classical primal-dual method, which is based on the logarithmic barrier method.

A two-point boundary value problem is considered on the interval [0, 1], where the leading term in the differential operator is a Caputo fractional derivative of order δ with 1 < δ < 2. Writing u for the solution of the problem, it is known that typically u′′(x) blows up as x→ 0. A numerical example demonstrates the possibility of a further phenomenon that imposes difficulties on numerical meth...