In this paper we present several \infeasible-start" path-following and potential-reduction primal-dual interior-point methods for nonlinear conic problems. These methods try to nd a recession direction of the feasible set of a self-dual homogeneous primal-dual problem. The methods under consideration generate an-solution for an-perturbation of an initial strictly (primal and dual) feasible prob...

An improved topology of a low-speed permanent magnet vernier machine called a dual-stator interior permanent magnet vernier machine (DS-IPMVM) is introduced to significantly increase torque density and power factor. Dual-stator is usually adopted in machine design for more torque and the abundant space utilization. Interior spoke-type magnet array in the rotor is designed for magnet flux focusi...

We propose and study a new method, called the Interior Epigraph Directions (IED) method, for solving constrained nonsmooth and nonconvex optimization. The IED method considers the dual problem induced by a generalized augmented Lagrangian duality scheme, and obtains the primal solution by generating a sequence of iterates in the interior of the dual epigraph. First, a deflected subgradient (DSG...

Nowadays, in the industrial environment of simulation-based design, optimization has been widely applied. This article illustrates that how truss structural frequency optimization problems is being solved by interior point trust region method (IPTRM). As a possible way, primal-dual interior point method could optimize the structure by multiple centrality modifications with trust region subprobl...

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...

The theory of self-scaled conic programming provides a uniied framework for the theories of linear programming, semideenite programming and convex quadratic programming with convex quadratic constraints. The standard search directions for interior-point methods applied to self-scaled conic programming problems are the so-called Nesterov-Todd directions. In this article we show that these direct...

Many practical optimization problems involve nonsmooth (that is, not necessarily differentiable) functions of hundreds or thousands of variables with various constraints. In this paper, we describe a new efficient adaptive limited memory interior point bundle method for large, possible nonconvex, nonsmooth inequality constrained optimization. The method is a hybrid of the nonsmooth variable met...

A generalized class of infeasible-interior-point methods for solving horizontal linear complementarity problem is analyzed and suucient conditions are given for the convergence of the sequence of iterates produced by methods in this class. In particular it is shown that the largest step path following algorithms generates convergent iterates even when starting from infeasible points. The comput...

We present a generalization of a homogeneous self-dual linear programming (LP) algorithm to solving the monotone complementarity problem (MCP). The algorithm does not need to use any \big-M" parameter or two-phase method, and it generates either a solution converging towards feasibility and complementarity simultaneously or a certiicate proving infeasibility. Moreover, if the MCP is polynomiall...

An example of SDPs (semide nite programs) exhibits a substantial di culty in proving the superlinear convergence of a direct extension of the Mizuno-Todd-Ye type predictorcorrector primal-dual interior-point method for LPs (linear programs) to SDPs, and suggests that we need to force the generated sequence to converge to a solution tangentially to the central path (or trajectory). A Mizuno-Todd...