In this paper, we are concerned with nonlinear minimization problems with second order cone constraints. A primal-dual interior point method is proposed for solving the problems. We also propose a new primal-dual merit function by combining the barrier penalty function and the potential function within the framework of the line search strategy, and show the global convergence property of our me...

We propose a unified framework for the update of the barrier parameter in interior-point methods for nonlinear programming. The original primal-dual system is augmented to incorporate explicitly an updating function. We analyze local convergence properties and recover known updating strategies as special cases. We report numerical experiments on nonlinear problems and compare our results to a s...

We present a primal-dual interior point method (IPM) for solving smooth convex optimization problems which arise during the placement of integrated circuits. The interior point method represents a substantial enhancement in flexibility verses other methods while having similar computational requirements. We illustrate that iterative solvers are efficient for calculation of search directions dur...

The convergence of the Tapia indicators for infeasible{interior{point methods for solving degenerate linear complementarity problems is investigated. A new estimate of the rate of convergence of the Tapia indicators for the indices where both primal and dual variables vanish in the solution is obtained, showing that Tapia indicators for these indices converge slower than for other indices. Use ...

In this paper we study interior point trajectories in semideenite programming (SDP) including the central path of an SDP. This work was inspired by the seminal work by Megiddo on linear programming trajectories 15]. Under an assumption of primal and dual strict feasibility , we show that the primal and dual central paths exist and converge to the analytic centers of the optimal faces of, respec...

Primal-dual path-following methods for constrained minimization problems in function space with low multiplier regularity are introduced and analyzed. Regularity properties of the path are proved. The path structure allows us to define approximating models, which are used for controlling the path parameter in an iterative process for computing a solution of the original problem. The Moreau–Yosi...