相关论文: A line search filter sequential adaptive cubic reg…
The scalable adaptive cubic regularization method ($\mathrm{ARC_{q}K}$: Dussault et al. in Math. Program. Ser. A 207(1-2): 191-225, 2024) has been recently proposed for unconstrained optimization. It has excellent convergence properties,…
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…
Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…
Adaptive cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems involving a shifted Hessian in the spirit of the Levenberg-Marquardt and trust-region methods. The standard approach consists in…
In this work we describe an Adaptive Regularization using Cubics (ARC) method for large-scale nonconvex unconstrained optimization using Limited-memory Quasi-Newton (LQN) matrices. ARC methods are a relatively new family of optimization…
We consider the Adaptive Regularization with Cubics approach for solving nonconvex optimization problems and propose a new variant based on inexact Hessian information chosen dynamically. The theoretical analysis of the proposed procedure…
We propose and analyze random subspace variants of the second-order Adaptive Regularization using Cubics (ARC) algorithm. These methods iteratively restrict the search space to some random subspace of the parameters, constructing and…
Adaptive regularization with cubics (ARC) is an algorithm for unconstrained, non-convex optimization. Akin to the popular trust-region method, its iterations can be thought of as approximate, safe-guarded Newton steps. For cost functions…
The cubic regularization method (CR) and its adaptive version (ARC) are popular Newton-type methods in solving unconstrained non-convex optimization problems, due to its global convergence to local minima under mild conditions. The main aim…
A sequential quadratic programming method is designed for solving general smooth nonlinear stochastic optimization problems subject to expectation equality constraints. We consider the setting where the objective and constraint function…
Adaptive cubic regularization methods have emerged as a credible alternative to linesearch and trust-region for smooth nonconvex optimization, with optimal complexity amongst second-order methods. Here we consider a general/new class of…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
A step-search sequential quadratic programming method is proposed for solving nonlinear equality constrained stochastic optimization problems. It is assumed that constraint function values and derivatives are available, but only stochastic…
A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that…
We focus on minimizing nonconvex finite-sum functions that typically arise in machine learning problems. In an attempt to solve this problem, the adaptive cubic regularized Newton method has shown its strong global convergence guarantees…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique,…
In this paper, we propose an infeasible arc-search interior-point algorithm for solving nonlinear programming problems. Most algorithms based on interior-point methods are categorized as line search, since they compute a next iterate on a…
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…