In this paper we develop several polynomial-time interior-point methods (IPM) for solving nonlinear primal-dual conic optimization problem. We assume that the barriers for the primal and the dual cone are not conjugate. This broken symmetry does not allow to apply the standard primal-dual IPM. However, we show that in this situation it is also possible to develop very efficient optimization met...

Several algorithms in optimization can be viewed as following a solution as a parameter or set of parameters is adjusted to a desired value. Examples include homotopy methods in complementarity problems and path-following (infeasible-) interior-point methods. If we have a metric in solution space that corresponds to the complexity of moving from one solution point to another, there is an induce...

in many infeasible linear programs it is important to construct it to a feasible problem with a minimum pa-rameters changing corresponding to a given nonnegative vector. this paper defines a new inverse problem, called “inverse feasible problem”. for a given infeasible polyhedron and an n-vector a minimum perturba-tion on the parameters can be applied and then a feasible polyhedron is concluded.

We introduce a twice differentiable augmented Lagrangian for nonlinear optimization with general inequality constraints and show that strict local minimizer of the original problem is an approximate solution Lagrangian. A novel method multipliers (ALM) then presented. Our originated from generalization Hestenes-Powell Lagrangian, combination interior-point technique. It shares similar algorithm...

This paper introduces the algorithmic design and implementation of Tulip, an open-source interior-point solver for linear optimization. It implements a regularized homogeneous algorithm with multiple centrality corrections, therefore handles unbounded infeasible problems. The is written in Julia, thus allowing flexible efficient implementation: Tulip's framework fully disentangled from algebra ...

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...

Sparse covariance selection problems can be formulated as log-determinant (log-det ) semidefinite programming (SDP) problems with large numbers of linear constraints. Standard primal-dual interior-point methods that are based on solving the Schur complement equation would encounter severe computational bottlenecks if they are applied to solve these SDPs. In this paper, we consider a customized ...

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...

In the field of single crystal plasticity, different algorithms exist for solution constitutive equations. They can be grouped into rate independent and dependent approaches, where both classes are governed by inherent shortcomings, as discussed in, e.g., [3]. This contribution outlines an algorithmic formulation plasticity at small strains case relying on infeasible primal-dual interior point ...