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Golden Ratio Algorithms for Variational Inequalities [article]

Yura Malitsky
2019 arXiv   pre-print
The paper presents a fully explicit algorithm for monotone variational inequalities.  ...  The operator F need not be Lipschitz-continuous, which also makes the algorithm interesting in the area of composite minimization where one cannot use the descent lemma.  ...  Golden Ratio Algorithms Let ϕ = √ 5+1 2 be the golden ratio, that is ϕ 2 = 1 + ϕ.  ... 
arXiv:1803.08832v2 fatcat:hezsfjdetzcv5lbwh6bxei432y

Golden ratio algorithms with new stepsize rules for variational inequalities [article]

Dang Van Hieu, Yeol Je Cho, Yi-bin Xiao
2019 arXiv   pre-print
In this paper, we introduce two golden ratio algorithms with new stepsize rules for solving pseudomonotone and Lipschitz variational inequalities in finite dimensional Hilbert spaces.  ...  Also, we give several numerical results to show the behavior of the algorithms in comparisons with other algorithms.  ...  Yura Malitsky for sending us the paper [6] .  ... 
arXiv:1904.07591v1 fatcat:idypcj2hsfbk3ooyq26gmt3j4u

A golden ratio primal-dual algorithm for structured convex optimization [article]

Xiaokai Chang, Junfeng Yang
2020 arXiv   pre-print
We design, analyze and test a golden ratio primal-dual algorithm (GRPDA) for solving structured convex optimization problem, where the objective function is the sum of two closed proper convex functions  ...  Moreover, we show for regularized least-squares and linear equality constrained problems that the reciprocal of the convex combination parameter can be extended from the golden ratio to 2 and meanwhile  ...  Given the nice convergence properties and the promising numerical results of golden ratio algorithm [22] , it is desirable to construct a Gauss-Seidel type golden ratio PDA for the saddle point problem  ... 
arXiv:1910.13260v6 fatcat:2shmanxxvjhezm6esjr5xgg7q4

Golden ratio algorithms for solving equilibrium problems in Hilbert spaces [article]

Nguyen The Vinh
2018 arXiv   pre-print
In this paper, we design a new iterative algorithm for solving pseudomonotone equilibrium problems in real Hilbert spaces.  ...  The advantage of our algorithm is that it requires only one strongly convex programming problem at each iteration.  ...  Acknowledgement The author would like to thank Yura Malitsky for sending him the paper [24] and for many useful comments.  ... 
arXiv:1804.01829v1 fatcat:pf4yweswwfaspcez2fe4xdygom

Flexible Regularized Estimating Equations: Some New Perspectives [article]

Yi Yang, Yuwen Gu, Yue Zhao, Jun Fan
2021 arXiv   pre-print
In this note, we make some observations about the equivalences between regularized estimating equations, fixed-point problems and variational inequalities.  ...  inequality; (c) Both equivalences extend to any estimating equations and any penalty functions.  ...  While fast computational algorithms are less developed for (4), there are many efficient solvers for fixed-point problems and variational inequalities.  ... 
arXiv:2110.11074v2 fatcat:6ccyjt77x5dz7hyzh5ysxv3g24

On the dual step length of the alternating direction method of multipliers [article]

Guoyong Gu, Junfeng Yang
2020 arXiv   pre-print
ratio, ruling out the possibility of breaking the golden ratio within this conventional analytic framework.  ...  However, it remains unclear whether the golden ratio can be exceeded in the general convex setting.  ...  extending γ beyond the golden ratio within this analytic framework.  ... 
arXiv:2006.08309v2 fatcat:q6ursjwmkvadxgsdelkpxdtjry

True Equalization of Polarization-Dependent Loss in Presence of Fast Rotation of SOP

Nan Cui, Xiaoguang Zhang, Wenbo Zhang, Xianfeng Tang, Lixia Xi
2020 Applied Sciences  
PDL causes a difference in signal power and imbalance of optical signal-to-noise ratio (OSNR) between the two polarization branches.  ...  Faced with this dilemma, in this paper, we propose a scheme for the true equalization of PDL in the presence of fast RSOP through an approach based on the combination of the polarization-time code and  ...  Sci. 2020, 10, x FOR PEER REVIEW 3 of 11 where and denote the amplitude ratio angle and phase difference, respectively.  ... 
doi:10.3390/app10113844 fatcat:fa3p7nqerrf47lnap3ez7ofwby

The convergence rate of a golden ratio algorithm for equilibrium problems [article]

Dang Van Hieu
2018 arXiv   pre-print
In this paper, we establish the R-linear rate of convergence of a golden ratio algorithm for solving an equilibrium problem in a Hilbert space.  ...  Several experiments are performed to show the numerical behavior of the algorithm and also to compare with others.  ...  Nguyen The Vinh for sending us the papers [16, 22] and for many valuable comments.  ... 
arXiv:1810.03564v1 fatcat:y42pcwcmu5bude3wuemorvwbku

Dilated Matrix Inequalities for Control Design in Systems with Actuator Constraint [article]

Solmaz Sajjadi-Kia, Faryar Jabbari
2013 arXiv   pre-print
In this paper, we present a new variation of dilated matrix inequalities (MIs) for Bounded Real MI, invariant set MI and constraint MI, for both state and output feedback synthesis problems.  ...  It is shown that for the resulting multi-objective saturation problem, the new form of dilated MIs achieves an upper bound for L_2 gain that is less than or equal to the upper bound estimate achieved by  ...  CONCLUSIONS We presented new dilated matrix inequalities for Bounded Real MI, invariant set MI and constraint MI.  ... 
arXiv:1302.3762v1 fatcat:7rwp7t5etbe4dhyd4dpdkjdpvi

Efficient Maximum Power Point Tracking Algorithm for PV Application under Rapid Changing Weather Condition

Khaled M. Bataineh, Amr Hamzeh
2014 ISRN Renewable Energy  
This study presents a novel search algorithm of maximum power point tracking for photovoltaic power generation systems.  ...  The performance of the developed algorithm, under extremely changing environmental conditions, is found to be superior compared to that of other conventional algorithms.  ...  The golden ratio which is equal to 1.61803398 makes the algorithm converge at a constant speed. Implementation for PV System. Theoretically, MMP falls between 0 V and oc max .  ... 
doi:10.1155/2014/673840 fatcat:oa7yunxecfhwpnoldizm5pldsa

An Algorithmic Framework of Generalized Primal–Dual Hybrid Gradient Methods for Saddle Point Problems

Bingsheng He, Feng Ma, Xiaoming Yuan
2017 Journal of Mathematical Imaging and Vision  
In particular, a completely symmetric PDHG scheme with the golden-ratio step sizes is included.  ...  We investigate the restriction onto these step sizes and conduct the convergence analysis for the algorithmic framework.  ...  Conclusions We propose an algorithmic framework of generalized primal-dual hybrid gradient (PDHG) methods for saddle point problems and study its convergence.  ... 
doi:10.1007/s10851-017-0709-5 fatcat:m6ay6wvjx5csvlanlhkqo5v6yq

Models and algorithms for the 2-dimensional cell suppression problem in statistical disclosure control

Matteo Fischetti, Juan José Salazar
1999 Mathematical programming  
Exact and heuristic separation procedures are also proposed and embedded within a branch-and-cut algorithm for the exact solution of the problem.  ...  The algorithm makes use of an efficient heuristic procedure to find near-optimal solutions.  ...  We thank Alberto Caprara for his help in code testing.  ... 
doi:10.1007/s10107980022a fatcat:tarfrl3rtndltg66ganjwp2o7a

Probe-level measurement error improves accuracy in detecting differential gene expression

X. Liu, M. Milo, N. D Lawrence, M. Rattray
2006 Bioinformatics  
A variational approximation is used for efficient parameter estimation. We compare this approximation with MAP and MCMC parameter estimation in terms of computational efficiency and accuracy.  ...  The method is used to calculate the probability of positive log-ratio (PPLR) of expression levels between conditions.  ...  reviewers for constructive comments.  ... 
doi:10.1093/bioinformatics/btl361 pmid:16820429 fatcat:xzxyr5ualjdl7blbpimmavnac4

Institutions, Partisanship, and Inequality in the Long Run

Kenneth Scheve, David Stasavage
2009 World Politics  
Their empirical results provide little support for the idea that either of these two factors is correlated with income inequality over this period.  ...  of the left are associated with lower levels of income inequality.  ...  the 90-10 earnings ratio.  ... 
doi:10.1017/s0043887109000094 fatcat:a44bzwocmfbpvichao774ey564

Hybrid Allocation of Capacitor and Distributed Static Compensator in Radial Distribution Networks Using Multi-Objective Improved Golden Ratio Optimization based on Fuzzy Decision Making

Alireza Noori, Yiming Zhang, Negar Nouri, M. Hajivand
2020 IEEE Access  
INDEX TERMS Radial distribution network, optimal capacitor and DSTATCOM allocation, power loss reduction factor, fuzzy decision making, multi-objective improved golden ratio optimization algorithm.  ...  Optimal location and size of reactive resources is determined based using multi-objective improved golden ratio optimization algorithm (MOIGROM) inspired by Fibonacci series and improved using nonlinearly  ...  GOLDEN RATIO OPTIMIZATION ALGORITHM (GROM) The growth of Creatures or physical phenomena such as tornadoes depends on their former conditions as a golden ratio based on the Fibonacci series, which improves  ... 
doi:10.1109/access.2020.2993693 fatcat:63ilpx6y4nhnfblnwmbgfmik5e
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