Related papers: An Infeasible Interior-point Arc-search Algorithm …
This paper proposes an infeasible interior-point algorithm for the convex optimization problem using arc-search techniques. The proposed algorithm simultaneously selects the centering parameter and the step size, aiming at optimizing the…
We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…
This paper proposes an arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc…
Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper…
Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally…
An arc-search interior-point method is a type of interior-point methods that approximates the central path by an ellipsoidal arc, and it can often reduce the number of iterations. In this work, to further reduce the number of iterations and…
In this paper, we propose an arc-search infeasible-interior-point algorithm. We show that this algorithm is polynomial and the polynomial bound is ${\cal O}(nL)$ which is at least as good as the best existing bound for…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
Nonlinear constrained optimization has a wide range of practical applications. In this paper, we consider nonlinear optimization with inequality constraints. The interior point method is considered to be one of the most powerful algorithms…
The work of Wachter and Biegler suggests that infeasible-start interior point methods (IPMs) developed for linear programming cannot be adapted to nonlinear optimization without significant modification, i.e., using a two-phase or penalty…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
In this paper, we study an infeasible interior-point method for linear optimization with full-Newton step. The introduced method uses an algebraic equivalent transformation on the centering equation of the system which defines the central…
Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…
Interior point methods are among the most popular techniques for large scale nonlinear optimization, owing to their intrinsic ability of scaling to arbitrary large problem sizes. Their efficiency has attracted in recent years a lot of…
Interior-point algorithms constitute a very interesting class of algorithms for solving linear-programming problems. In this paper we study efficient implementations of such algorithms for solving the linear program that appears in the…
We develop an interior-point method for nonsmooth regularized bound-constrained optimization problems. Our method consists of iteratively solving a sequence of unconstrained nonsmooth barrier subproblems. We use a variant of the proximal…
Identifying optimal basic feasible solutions to linear programming problems is a critical task for mixed integer programming and other applications. The crossover method, which aims at deriving an optimal extreme point from a suboptimal…
In this paper, a sequential adaptive regularization algorithm using cubics (ARC) is presented to solve nonlinear equality constrained optimization. It is motivated by the idea of handling constraints in sequential quadratic programming…