Abstract In this paper, we revisit some elements of the theory self-concordant functions. We replace notion barrier by a new set-limited function, which forms wider class. show that proper functions ensure polynomial time complexity corresponding path-following method (PFM). Our PFM follows deviated path, connects an arbitrary feasible point with solution problem. present applications our appro...

Applying an interior-point method to the central-path conditions is a widely used approach for solving quadratic programs. Reformulating these in log-domain natural variation on this that our knowledge previously unstudied. In paper, we analyze methods and prove their polynomial-time convergence. We also they are approximated by classical barrier precise sense provide simple computational exper...

A primal-dual interior point method for optimal control problems is considered. The algorithm is directly applied to the infinite dimensional problem. Existence and convergence of the central path are analyzed, and linear convergence of a short step pathfollowing method is established.

The Semidefinite Program (SDP) is a fundamental problem in mathematical programming. It covers a wide range of applications, such as combinatorial optimization, control theory, polynomial optimization, and quantum chemistry. Solving extremely large-scale SDPs which could not be solved before is a significant work to open up a new vista of future applications of SDPs. Our two software packages S...