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A Family of Multi-parameterized Proximal Point Algorithms

Jianchao Bai, Ke Guo, Xiaokai Chang
2019 IEEE Access  
In this paper, a multi-parameterized proximal point algorithm combining with a relaxation step is developed for solving convex minimization problem subject to linear constraints.  ...  INDEX TERMS Convex optimization, proximal point algorithm, complexity, signal processing.  ...  INTRODUCTION We focus on the following convex minimization problem with linear equality constraints min f (x) s.t.  ... 
doi:10.1109/access.2019.2952155 fatcat:ovx5y76gzfcpfh7jlixgqe6xue

An Implementable First-Order Primal-Dual Algorithm for Structured Convex Optimization

Feng Ma, Mingfang Ni, Lei Zhu, Zhanke Yu
2014 Abstract and Applied Analysis  
We show that the proposed method can be interpreted as a proximal point algorithm with a customized metric proximal parameter.  ...  Many application problems of practical interest can be posed as structured convex optimization models. In this paper, we study a new first-order primaldual algorithm.  ...  Our algorithm can be viewed as a customized proximal point method with a special proximal regularization parameter.  ... 
doi:10.1155/2014/396753 fatcat:4onz3raem5exfmxsc2bq5ow3ve

Convex optimization techniques in system identification

Lieven Vandenberghe
2012 IFAC Proceedings Volumes  
algorithms for large-scale nondifferentiable convex optimization.  ...  This interest is motivated by the success of convex methods for sparse optimization and rank minimization in signal processing, statistics, and machine learning, and by the development of new classes of  ...  Proximal gradient algorithms The proximal gradient algorithm is an extension of the gradient algorithm to problems with simple constraints or with simple nondifferentiable terms in the cost function.  ... 
doi:10.3182/20120711-3-be-2027.00244 fatcat:k4dxky3ktre47hoagl7smuskca

Some Recent Trends in Variational Inequalities and Optimization Problems with Applications

Abdellah Bnouhachem, Abdelouahed Hamdi, Xu Minghua
2014 Abstract and Applied Analysis  
Fu presents an implementable proximal step by a slight relaxation to the subproblem of proximal point algorithm (PPA) to solve linearly constrained convex programming.  ...  proximal point algorithm to the dual problem of a constrained optimization problem.  ...  Acknowledgments We would like to express our sincere thanks to the authors for contributing to this issue, as well as to the anonymous reviewers for their generous and accurate refereeing process and their  ... 
doi:10.1155/2014/215098 fatcat:en777oognrd6najx2lmafhw5qm

Low-Complexity Modeling of Partially Available Second-Order Statistics: Theory and an Efficient Matrix Completion Algorithm

Armin Zare, Yongxin Chen, Mihailo R. Jovanovic, Tryphon T. Georgiou
2017 IEEE Transactions on Automatic Control  
We interpret AMA as a proximal gradient for the dual problem and prove sub-linear convergence for the algorithm with fixed step-size.  ...  For problem sizes that these solvers cannot handle, we develop a customized alternating minimization algorithm (AMA).  ...  In fact, we show that our algorithm works as a proximal gradient on the dual problem and establish a sub-linear convergence rate for the fixed step-size.  ... 
doi:10.1109/tac.2016.2595761 fatcat:muooljzshjcizfinnxvse4fgom

A Splitting Method for Optimal Control

Brendan O'Donoghue, Giorgos Stathopoulos, Stephen Boyd
2013 IEEE Transactions on Control Systems Technology  
We apply an operator splitting technique to a generic linear-convex optimal control problem, which results in an algorithm that alternates between solving a quadratic control problem, for which there are  ...  Index Terms-Alternating directions method of multipliers (ADMM), convex optimization, embedded control, fixed point algorithms for control, model predictive control (MPC), operator splitting, optimal control  ...  Wang for helpful discussions and feedback. The authors would also like to thank three anonymous reviewers for their thoughtful and constructive feedback.  ... 
doi:10.1109/tcst.2012.2231960 fatcat:nmf7zmdyenbpthb2lvicxvqwdm

Alternating direction optimization algorithms for covariance completion problems

Armin Zare, Mihailo R. Jovanovic, Tryphon T. Georgiou
2015 2015 American Control Conference (ACC)  
We develop customized algorithms based on alternating direction methods that are wellsuited for large scale problems.  ...  Thus, it is of interest to complete partially specified covariance matrices in a way that is consistent with the linearized dynamics.  ...  The choice of We now focus on the performance of customized alternating minimization algorithm. For 50 masses and γ = 2.2 we use the algorithm discussed in Section IV-B to solve (CP) with = 10 −3 .  ... 
doi:10.1109/acc.2015.7170787 dblp:conf/amcc/ZareJG15 fatcat:ovs4zgca4nhf7gdh26q2ayqve4

Sensor Fault Diagnosis

Giorgos Stathopoulos, Harsh Shukla, Alexander Szucs, Ye Pu, Colin N. Jones
2016 Foundations and Trends® in Systems and Control  
Acknowledgements We would like to thank Jean-Hubert Hours for contributing to this manuscript with his knowledge in noncnovex optimization and Ivan Pejcic for thorough readings in the early stages of this  ...  We are also grateful to Panos Patrinos, Pontus Giselsson and the anonymous reviewers for their very useful comments and suggestions.  ...  The operator is evaluated at a given point x and looks for a minimizer that makes a compromise between the minimizer of the function f and the point x.  ... 
doi:10.1561/2600000008 fatcat:btvndyfrvzgt7l22l3gvsy767e

Proximal algorithms for large-scale statistical modeling and optimal sensor/actuator selection [article]

Armin Zare, Hesameddin Mohammadi, Neil K. Dhingra, Mihailo R. Jovanović, Tryphon T. Georgiou
2019 arXiv   pre-print
We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate  ...  To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods.  ...  We prove linear convergence for the proximal gradient algorithm with fixed step-size and propose an adaptive step-size selection method that can improve convergence.  ... 
arXiv:1807.01739v3 fatcat:ji5q5nkntjgs7mkxdwzijnm4ry

A User-Friendly Computational Framework for Robust Structured Regression with the L_2 Criterion [article]

Jocelyn T. Chi, Eric C. Chi
2021 arXiv   pre-print
In addition to introducing an algorithm for performing L_2E regression, our framework enables robust regression with the L_2 criterion for additional structural constraints, works without requiring complex  ...  We introduce a user-friendly computational framework for implementing robust versions of a wide variety of structured regression methods with the L_2 criterion.  ...  As long as the structural constraints or penalties satisfy convexity and continuity conditions, a solution obtained with our framework is guaranteed to converge to a first order stationary point.  ... 
arXiv:2010.04133v2 fatcat:7xr4wc2cejc6jptquuru3tdxdy

Combining Method of Alternating Projections and Augmented Lagrangian for Task Constrained Trajectory Optimization [article]

Arun Kumar Singh, Reza Ghabcheloo, Andreas Muller, Harit Pandya
2018 arXiv   pre-print
At the core of our approach are some simple reformulations, which when coupled with the method of alternating projection, leads to an efficient convex optimization based routine for computing a feasible  ...  In this paper, we present a novel custom optimizer which exploits the underlying structure present in many task constraints.  ...  Each minimization in algorithm 2 is a convex QP problem with simple box bounds on the optimization variables and thus, can be solved analytically.  ... 
arXiv:1803.03784v1 fatcat:xyqzf7fgrnb5foz4v3gjzfogw4

Page 6838 of Mathematical Reviews Vol. , Issue 94k [page]

1994 Mathematical Reviews  
For analyzing the inner loop iterations, the authors employ a proximity measure of noncentral points stud- ied by C. Roos and J.-P. Vial [Math. Programming 54 (1992), no. 3, Ser.  ...  Tomomi (J-TOKYTE-SS; Meguro) Parametric simplex algorithms for solving a special class of nonconvex minimization problems.  ... 

Handling convexity-like constraints in variational problems [article]

Quentin Mérigot
2014 arXiv   pre-print
We show how these discretizations are well suited for the numerical solution of problems of calculus of variations under convexity constraints.  ...  This framework applies to the approximation of convex functions by piecewise linear functions on a mesh of the domain and by other finite-dimensional spaces such as tensor-product splines.  ...  The first named author would like to thank Robert McCann for introducing him to the principal-agent problem and Young-Heon Kim for interesting discussions.  ... 
arXiv:1403.2340v1 fatcat:rh4cvep7szgrxlyavhci76csnq

Handling Convexity-Like Constraints in Variational Problems

Quentin Mérigot, Édouard Oudet
2014 SIAM Journal on Numerical Analysis  
We show how these discretizations are well suited for the numerical solution of problems of calculus of variations under convexity constraints.  ...  This framework applies to the approximation of convex functions by piecewise-linear functions on a mesh of the domain and by other finite-dimensional spaces such as tensor-product splines.  ...  The first author would like to thank Robert McCann for introducing him to the principal-agent problem and Young-Heon Kim for interesting discussions.  ... 
doi:10.1137/130938359 fatcat:3w4pbo2l7fgf7mhck5s7m7dyey

Page 2327 of Mathematical Reviews Vol. , Issue 91D [page]

1991 Mathematical Reviews  
Summary: “An algorithm for solving a linear programming prob- lem for which the number of constraints is considerably greater than the number of variables is proposed.  ...  [Wright, Stephen Joseph] (1-NCS) Implementing proximal point methods for linear programming. J. Optim. Theory Appl. 65 (1990), no. 3, 531-554.  ... 
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