The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization

Wei, Zengxin; Yu, Gaohang; Yuan, Gonglin; Lian, Zhigang

doi:10.1023/b:coap.0000044184.25410.39

Cited by 100 publications

(64 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In fact, the practical computation shows that this method is better than the normal BFGS method (see [41,42] for detail) for some given problems [30]. Furthermore, some theoretical advantages of the new quasi-Newton equation (2.6) can be seen from the following two theorems.…”

Section: 2)mentioning

confidence: 94%

See 1 more Smart Citation

Modified Limited Memory BFGS Method With Nonmonotone Line Search for Unconstrained Optimization

Yuan¹,

Wei²,

Wu³

2010

Journal of the Korean Mathematical Society

Self Cite

View full text Add to dashboard Cite

show abstract

Section: 2)mentioning

confidence: 94%

“…It is not difficult to deduce that s T k y 2 * k > 0 holds for the uniformly convex function f (or see [42]). We all know that the condition s T k y 2 * k > 0 can ensure that the update matrix B k+1 from (2.8) inherits the positive definiteness of B k .…”

Section: 2)mentioning

confidence: 99%

Modified Limited Memory BFGS Method With Nonmonotone Line Search for Unconstrained Optimization

Yuan¹,

Wei²,

Wu³

2010

Journal of the Korean Mathematical Society

Self Cite

View full text Add to dashboard Cite

show abstract

“…Numerical results reported in [8] suggest that improvements have been achieved. Along this line, Xiao et al [19] proposed another two choices of β k by introducing two modified quasi-Newton secant equations developed in [22,18]. Numerical experiments show that their method seems to be better.…”

Section: Smooth Bound Constrained Optimizationmentioning

confidence: 99%

Learning Unknown Structure in CRFs via Adaptive Gradient Projection Method

Xue

Zhang

2016

Stat., optim. inf. comput.

View full text Add to dashboard Cite

This paper focuses on learning unknown structure in conditional random fields (CRFs), especially learning both the structure and parameters of a CRF model simultaneously. By adding the l 2 -regularization to node parameters and the group l 1 -regularization to edge parameters, this structure learning problem can be cast as a convex minimization problem. Then an adaptive gradient method is proposed to solve the minimization problem. Extensive simulation experiments are presented to show the performance of the proposed approach for learning unknown structure.

show abstract

“…The Broyden-Fletcher-Goldfarb-Shanno (BFGS) [68] algorithm (A11) has been a classical optimization algorithm belonging to the class of approximate Newton methods. Along with several variants [66,63,35,32], BFGS has been widely used in the domain of unconstrained optimization. The Method of Moving Asymptotes (MMA) algorithm (A24) by Svanberg [57] is based on locally approximating the gradient of the objective function and a quadratic penalty term.…”

Section: (A29)mentioning

confidence: 99%

Benchmarking NLopt and state-of-the-art algorithms for continuous global optimization via IACOR

Kumar

Soman

Jayadeva

2016

Swarm and Evolutionary Computation

View full text Add to dashboard Cite

This paper presents a comparative analysis of the performance of the Incremental Ant Colony algorithm for continuous optimization (IACO R ), with different algorithms provided in the NLopt library. The key objective is to understand how the various algorithms in the NLopt library perform in combination with the Multi Trajectory Local Search (Mtsls1) technique. A hybrid approach has been introduced in the local search strategy by the use of a parameter which allows for probabilistic selection between Mtsls1 and a NLopt algorithm. In case of stagnation, the algorithm switch is made based on the algorithm being used in the previous iteration. The paper presents an exhaustive comparison on the performance of these approaches on Soft Computing (SOCO) and Congress on Evolutionary Computation (CEC) 2014 benchmarks. For both benchmarks, we conclude that the best performing algorithm is a hybrid variant of Mtsls1 with BFGS for local search.

show abstract

The Superlinear Convergence of a Modified BFGS-Type Method for Unconstrained Optimization

Cited by 100 publications

References 12 publications

Modified Limited Memory BFGS Method With Nonmonotone Line Search for Unconstrained Optimization

Modified Limited Memory BFGS Method With Nonmonotone Line Search for Unconstrained Optimization

Learning Unknown Structure in CRFs via Adaptive Gradient Projection Method

Benchmarking NLopt and state-of-the-art algorithms for continuous global optimization via IACOR

Contact Info

Product

Resources

About