This paper proposes an infeasible interior-point algorithm with full Nesterov-Todd step for second-order cone programming, which is an extension of the work of Roos (SIAM J. Optim., 16(4):1110–1136, 2006). The polynomial bound coincides with that of infeasible interior-point methods for linear programming, namely, O(l log l/ε).

In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on methods are categorized as line search since they compute a next iterate straight determined by direction which approximates the central path. The proposed uses arc approximation. We discuss convergence properties of algorithm. also conduct numerical e...

Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization due ...

In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primalinfeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is show...

In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal infeasible dual feasible inexact interior point method for multi-objective linear network flow problems. Our algorithm is contrasted with standard interior point methods and experimental results on...

Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deteministic equivalent of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of...

In this paper we present a primal-dual interior-point algorithm to solve a class of multi-objective network flow problems. More precisely, our algorithm is an extension of the single-objective primal-dual infeasible and inexact interior point method for multi-objective linear network flow problems. A comparison with standard interior point methods is provided and experimental results on bi-obje...