In this paper, we examine stability issues that arise when computing the search directions (Ax, Ay, As) for a primal-dual path-following interior point method for linear programming. The dual step Ay can be obtained by solving a weighted least-squares problem for which the weight matrix becomes extremely ill conditioned near the boundary of the feasible region. Hough and Vavasis proposed using ...

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...

Extending our previous work Monteiro and Pang (1996), this paper studies properties of two fundamental mappings associated with the family of interior-point methods for solving monotone nonlinear complementarity problems over the cone of symmetric positive semideenite matrices. The rst of these maps lead to a family of new continuous trajectories which include the central trajectory as a specia...

Recently, infeasibility issues in interior methods for nonconvex nonlinear programming have been studied. In particular, it has been shown how many line-search interior methods may converge to an infeasible point which is on the boundary of the feasible region with respect to the inequality constraints. The convergence is such that the search direction does not tend to zero, but the step length...

We present an algorithm for the constrained saddle point problem with a convexconcave function L and convex sets with nonempty interior. The method consists of moving away from the current iterate by choosing certain perturbed vectors. The values of gradients of L at these vectors provide an appropriate direction. Bregman functions allow us to define a curve which starts at the current iterate ...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasibl...

The attainable-region approach for reaction, mixing, and separation is applied for step-growth melt polycondensations. A concentration-based formulation is applied to develop hybrid reactorseparator models for the two-phase continuous stirred tank reactor and plug-flow reactor with simultaneous vapor removal. The evaporation of the volatile byproducts, which is typically limited by liquid-phase...