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Inexact Nonconvex Newton-Type Methods [PDF]
INFORMS Journal on Optimization, 2021 The paper aims to extend the theory and application of nonconvex Newton-type methods, namely trust region and cubic regularization, to the settings in which, in addition to the solution of subproblems, the gradient and the Hessian of the objective function are approximated. Using certain conditions on such approximations, the paper establishes optimal
Zhewei Yao +3 more
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Newton-type multilevel optimization method [PDF]
Optimization Methods and Software, 2019 Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the optimization model, and as a result, they outperform single-level methods, especially for large-scale models.
Chin Pang Ho +2 more
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Gauss–Newton-type methods for bilevel optimization [PDF]
Computational Optimization and Applications, 2021 AbstractThis article studies Gauss–Newton-type methods for over-determined systems to find solutions to bilevel programming problems. To proceed, we use the lower-level value function reformulation of bilevel programs and consider necessary optimality conditions under appropriate assumptions.
Jörg Fliege +2 more
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A Newton‐type method and its application [PDF]
International Journal of Mathematics and Mathematical Sciences, 2006 We prove an existence and uniqueness theorem for solving the operator equation F(x) + G(x) = 0, where F is a continuous and Gâteaux differentiable operator and the operator G satisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified ...
V. Antony Vijesh, P. V. Subrahmanyam
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Newton-type methods for simultaneous matrix diagonalization
Calcolo, 2022 This paper proposes a Newton-type method to solve numerically the eigenproblem of several diagonalizable matrices, which pairwise commute. A classical result states that these matrices are simultaneously diagonalizable. From a suitable system of equations associated to this problem, we construct a sequence that converges quadratically towards the ...
Khouja, Rima +2 more
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Journal of Complexity, 2010 Inexact Newton-type methods are discussed for approximating a locally unique solution of the nonlinear equation \(A(x)^{\#}(F(x)+G(x))=0\) in Banach space. Here \(F\) is a Fréchet-differentiable operator, \(G\) is a continuous operator and \(A(x)^{\#}\) is an analog of the Moore-Penrose generalized inverse of \(A(x)\) which is an approximation of the ...
Ioannis K. Argyros, Saïd Hilout
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FedDANE: A Federated Newton-Type Method [PDF]
2019 53rd Asilomar Conference on Signals, Systems, and Computers, 2019 Asilomar Conference on Signals, Systems, and Computers ...
Tian Li 0005 +5 more
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On a Newton‐Type Method for Differential‐Algebraic Equations [PDF]
Journal of Applied Mathematics, 2012 This paper deals with the approximation of systems of differential‐algebraic equations based on a certain error functional naturally associated with the system. In seeking to minimize the error, by using standard descent schemes, the procedure can never get stuck in local minima but will always and steadily decrease the error until getting to the ...
Sergio Amat +2 more
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Newton-type Methods for Minimax Optimization
CoRR, 2020 Differential games, in particular two-player sequential zero-sum games (a.k.a. minimax optimization), have been an important modeling tool in applied science and received renewed interest in machine learning due to many recent applications, such as adversarial training, generative models and reinforcement learning.
Guojun Zhang +3 more
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DINO: Distributed Newton-Type Optimization Method [PDF]
, 2020 We present a novel communication-efficient Newton-type algorithm for finite-sum optimization over a distributed computing environment. Our method, named DINO, overcomes both theoretical and practical shortcomings of similar existing methods. Under minimal assumptions, we guarantee global sub-linear convergence of DINO to a first-order stationary point ...
Crane, Rixon, Roosta, Fred
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