A generalization of the weighted central path{following method for convex quadratic programming is presented. This is done by uniting and modifying the main ideas of the weighted central path{following method for linear programming and the interior point methods for convex quadratic programming. By means of the linear approximation of the weighted logarithmic barrier function and weighted inscr...

We analyze a primal-dual interior-point method for nonlinear programming. We prove the global convergence for a wide class of problems under the standard assumptions on the problem.

This paper proposes a hybrid computational method (DIPS method) which works as a simplex method for solving a standard form linear program, and, simultaneously, as an interior point method for solving its dual. The DIPS method generates a sequence of primal basic feasible solutions and a sequence of dual interior feasible solutions interdependently. Along the sequences, the duality gap decrease...

In a second-order cone program (SOCP) a linear function is minimized over the intersection of an a ne set and the product of second-order (quadratic) cones. SOCPs are nonlinear convex problems that include linear and (convex) quadratic programs as special cases, but are less general than semide nite programs (SDPs). Several e cient primal-dual interior-point methods for SOCP have been developed...

Nonlinear semidefinite programming (SDP) problems have received a lot of attentions because of large variety of applications. In this paper, we survey numerical methods for solving nonlinear SDP problems. Three kinds of typical numerical methods are described; augmented Lagrangian methods, sequential SDP methods and primal-dual interior point methods. We describe their typical algorithmic forms...

Interior-point methods in semidefinite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions. Safeguards are typically required in order to handle rank-deficient Jacobians and free variables. We generalize the primal-dual regularization of Friedlander and Orban (2012) to SDP and show that it is possible to recover an optimal soluti...

We present a primal-dual interior point algorithm of line-search type for nonlinear programs, which uses a new decomposition scheme of sequential quadratic programming. The algorithm can circumvent the convergence difficulties of some existing interior point methods. Global convergence properties are derived without assuming regularity conditions. The penalty parameter ρ in the merit function i...

The computational burden of primal-dual interior point methods for linear programming relies on the computation of the search direction by solving one or more linear systems per iterations. The objective of this work is to study an efficient and robust way of solving these systems for large-scale sparse problems. Our proposal combines the use of the stable system and a hybrid iterative method w...

We analyse the scaling matrix, search direction, and neighbourhood used in MOSEK's algorithm for nonsymmetric conic optimization [J. Dahl E.D. Andersen, A primal-dual interior-point f...