Smoothing Newton algorithm for the circular cone programming with a nonmonotone line search

Chi, Xiaoni; Wei, Hongjin; Wan, Zhongping; Zhu, Zhibin

doi:10.1016/s0252-9602(17)30072-3

Cited by 5 publications

(1 citation statement)

References 25 publications

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“…For this reason, the semismooth Newton method can be used to solve such systems. The concept of the semismooth Newton method has been introduced first by Pang and Qi (1993), Qi (1993) and Qi and Sun (1993) and then developed in many papers and books (Chen et al, 2000; Chi et al, 2017; Hinze et al, 2008; Ito and Kunisch, 2008; Kröner et al, 2011). The semismooth Newton iteration can be stated regarding an active set strategy and the generalized derivatives of the max and min operators.…”

Section: Nsn Methods To Solve the Obtained Bound Constrained Optimizatmentioning

confidence: 99%

An adaptive semismooth Newton method for approximately solving control-constrained elliptic optimal control problems

Fard

Borzabadi

Sarani

2019

Transactions of the Institute of Measurement and Control

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The main goal of this paper is to study, analyse and prove the global convergence property of a nonmonotone semismooth Newton method. Based on this property, we aim to exploit an adaptive nonmonotone line search method and apply it for the approximate solution of elliptic optimal control problems with control constraints. To this end, we first convert the optimal control problem to a bound constrained optimization problem by using a finite-difference discretization scheme and a Newton–Cotes rule. Then we implement the adaptive nonmonotone semismooth Newton method to the resulting bound constrained optimization problem. We give some numerical examples to demonstrate the validity, efficiency and applicability of the presented method.

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Section: Nsn Methods To Solve the Obtained Bound Constrained Optimizatmentioning

confidence: 99%

An adaptive semismooth Newton method for approximately solving control-constrained elliptic optimal control problems

Fard

Borzabadi

Sarani

2019

Transactions of the Institute of Measurement and Control

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An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems

Tang

Zhou²,

Zhang³

2022

J Optim Theory Appl

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An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems

Fard

Sarani

Nosratipour

2019

Bull. Iran. Math. Soc.

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Smoothing Newton algorithm for the circular cone programming with a nonmonotone line search

Cited by 5 publications

References 25 publications

An adaptive semismooth Newton method for approximately solving control-constrained elliptic optimal control problems

An adaptive semismooth Newton method for approximately solving control-constrained elliptic optimal control problems

An Accelerated Smoothing Newton Method with Cubic Convergence for Weighted Complementarity Problems

An Efficient Nonmonotone Method for State-Constrained Elliptic Optimal Control Problems

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