相关论文: An infeasible interior-point arc-search method wit…
In this study, we consider the numerical solution of large systems of linear equations obtained from the stochastic Galerkin formulation of stochastic partial differential equations. We propose an iterative algorithm that exploits the…
In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…
We consider structured minimization problems subject to smooth inequality constraints and present a flexible algorithm that combines interior point (IP) and proximal gradient schemes. While traditional IP methods cannot cope with nonsmooth…
The existing machine learning algorithms for minimizing the convex function over a closed convex set suffer from slow convergence because their learning rates must be determined before running them. This paper proposes two machine learning…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
We introduce a generic scheme for accelerating first-order optimization methods in the sense of Nesterov, which builds upon a new analysis of the accelerated proximal point algorithm. Our approach consists of minimizing a convex objective…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We present a head-to-head evaluation of the Improved Inexact--Newton--Smart (INS) algorithm against a primal--dual interior-point framework for large-scale nonlinear optimization. On extensive synthetic benchmarks, the interior-point method…
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution. This result is proven both for an a…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
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…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
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…
Benson's outer approximation algorithm and its variants are the most frequently used methods for solving linear multiobjective optimization problems. These algorithms have two intertwined components: one-dimensional linear optimization one…
We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…
We present a unifying framework for adapting the update direction in gradient-based iterative optimization methods. As natural special cases we re-derive classical momentum and Nesterov's accelerated gradient method, lending a new intuitive…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
We propose a new framework to implement interior point method (IPM) to solve very large linear programs (LP). Traditional IPMs typically use Newton's method to approximately solve a subproblem that aims to minimize a log-barrier penalty…