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A Primal-Dual Active-Set Method for Non-Negativity Constrained Total Variation Deblurring Problems

D. Krishnan, Ping Lin, Andy M. Yip
2007 IEEE Transactions on Image Processing  
The contribution of our work is a fast and robust numerical algorithm to solve the non-negatively constrained problem.  ...  Here, dual refers to a combination of the Lagrangian and Fenchel duals. To solve the constrained primal-dual program, we use a semi-smooth Newton's method.  ...  Defeng for useful discussions on semi-smooth Newton's methods.  ... 
doi:10.1109/tip.2007.908079 pmid:17990753 fatcat:723pkwa44zcqpemgfez3naqa2q

Page 6358 of Mathematical Reviews Vol. , Issue 95j [page]

1995 Mathematical Reviews  
A, 53-76. 95j:90055b 90C25 65K05 Zhu, Ci You (1-NW-E; Evanston, IL) Erratum: “Solving large-scale minimax problems with the primal-dual steepest descent algorithm”. Math.  ...  Moreover, if y solves the dual problem then x = A’y/e solves the primal problem and P(A’y)/e) = D(y).  ... 

Linear matrix inequalities with chordal sparsity patterns and applications to robust quadratic optimization

Martin S. Andersen, Lieven Vandenberghe, Joachim Dahl
2010 2010 IEEE International Symposium on Computer-Aided Control System Design  
The algorithms take advantage of fast recursive algorithms for evaluating the function values and derivatives for the logarithmic barrier functions of the cone of positive semidefinite matrices with a  ...  As a specific application, we discuss robust quadratic optimization.  ...  Here we will take robust quadratically constrained quadratic programming (QCQP) and robust least-squares (RLS) as examples, and we demonstrate with some numerical experiments that the chordal matrix algorithms  ... 
doi:10.1109/cacsd.2010.5612788 dblp:conf/cacsd/AndersenVD10 fatcat:effa7wzdynenvd6ljrc5jmvl3u

A numerically stable dual method for solving strictly convex quadratic programs

D. Goldfarb, A. Idnani
1983 Mathematical programming  
The performance of the dual algorithm is compared against that of primal algorithms when nsed to solve randomly generated test problems and quadratic programs generated in the course of solving nonlinear  ...  programming problems by a successive quadratic programming code (the principal motivation for the development of the algorithm).  ...  Several approaches and numerous algorithms have been proposed for solving quadratic programming problems.  ... 
doi:10.1007/bf02591962 fatcat:ws4w4kat7jbbrh6hx6xf4cdfcy

On a primal-dual Newton proximal method for convex quadratic programs

Alberto De Marchi
2022 Computational optimization and applications  
AbstractThis paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method.  ...  QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.  ...  k ⊤ − , 1 16 On a primal-dual Newton proximal method for convex quadratic… (iii) Conversely, suppose ⋆ solves (4).  ... 
doi:10.1007/s10589-021-00342-y fatcat:hx7paeav5fhoziu2i36qtmwmqe

Page 7085 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
The authors contend that the numerical experiments support the view that interior-point methods provide an efficient tool for solving certain classes of convex programming problems. R. N.  ...  For the variants with the second update scheme, a much sharper estimation for the rate of convergence is obtained due to the new primal-dual feedback pattern. C.  ... 

A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

Tony F. Chan, Gene H. Golub, Pep Mulet
1999 SIAM Journal on Scientific Computing  
We present a new method for solving total variation (TV) minimization problems in image restoration.  ...  We caution that our use of the name primal-dual is based on a duality principle applied to the TVnorm (to be explained in more detail in Section 4) and should not be confused with the popular algorithms  ...  We would like to thank Andy Conn and Michael Overton for making their preprint 9] available to us, and Jun Zou for many helpful conversations on mixed nite elements with the rst author.  ... 
doi:10.1137/s1064827596299767 fatcat:4yrsdwcvbrb6xbil34z6vzme5m

An augmented Lagrangian approach to non-convex SAO using diagonal quadratic approximations

Albert A. Groenwold, L. F. P. Etman, Schalk Kok, Derren W. Wood, Simon Tosserams
2008 Structural And Multidisciplinary Optimization  
The results suggest that transformation of large-scale optimization problems with only a few constraints to a dual form via convexification need sometimes not be required, since this may equally well be  ...  The nonconvex subproblems are solved using an augmented Lagrangian (AL) strategy, rather than the Falk-dual, which is the norm in SAO based on convex subproblems.  ...  This may however also suggest that solution of a primal problem subject to simple bound constraints only, may be a computationally viable alternative to solving a Falklike dual problem, possibly even for  ... 
doi:10.1007/s00158-008-0304-x fatcat:csrc55ppz5bqjd5r7eqtmnsori

Faster minimization of linear wirelength for global placement

C.J. Alpert, T.F. Chan, A.B. Kahng, I.L. Markov, P. Mulet
1998 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
Our Primal-Dual Newton iteration stably attains quadratic convergence, making it a superior choice for implementing a placer such a s G O R D I A N -L , o r f o r a n y linear wirelength optimization.  ...  Other novel numerical methods described in the paper, the Primal Newton iteration and the Primal-Dual Newton iteration, further improve upon the linearly convergent W eiszfeld iteration.  ...  To nd an initial approximation close to the quadratic convergence region, one can solve a few linear systems as if using the Weiszfeld algorithm, then switch t o Primal-Dual iterations 13 .  ... 
doi:10.1109/43.673628 fatcat:gxrqmydu5bdopefxp7xd5sdd6i

Faster minimization of linear wirelength for global placement

Charles J. Alpert, Tony F. Chan, Dennis J.-H. Huang, Andrew B. Kahng, Igor L. Markov, Pep Mulet, Kenneth Yan
1997 Proceedings of the 1997 international symposium on Physical design - ISPD '97  
Our Primal-Dual Newton iteration stably attains quadratic convergence, making it a superior choice for implementing a placer such a s G O R D I A N -L , o r f o r a n y linear wirelength optimization.  ...  Other novel numerical methods described in the paper, the Primal Newton iteration and the Primal-Dual Newton iteration, further improve upon the linearly convergent W eiszfeld iteration.  ...  To nd an initial approximation close to the quadratic convergence region, one can solve a few linear systems as if using the Weiszfeld algorithm, then switch t o Primal-Dual iterations 13 .  ... 
doi:10.1145/267665.267670 dblp:conf/ispd/AlpertCHKMMY97 fatcat:buxae6hvgvd67fhtasmyh7gxja

B-preconditioned minimization algorithms for variational data assimilation with the dual formulation

S. Gürol, A. T. Weaver, A. M. Moore, A. Piacentini, H. G. Arango, S. Gratton
2013 Quarterly Journal of the Royal Meteorological Society  
Each sub-problem can be solved using a primal approach, where the minimization is performed in a space spanned by vectors of the size of the model control vector, or a dual approach, where the minimization  ...  First, the dimension of the minimization problem with the dual formulation does not increase when additional control variables, such as those accounting for model error in a weak-constraint formulation  ...  Acknowledgements This work is a contribution to the ADTAO and FILAOS projects which are financed by the RTRA STAE foundation.  ... 
doi:10.1002/qj.2150 fatcat:5yoepdl5zndjnpxane6ozgpyxe

A semi-proximal augmented Lagrangian based decomposition method for primal block angular convex composite quadratic conic programming problems [article]

Xin-Yee Lam, Defeng Sun, Kim-Chuan Toh
2018 arXiv   pre-print
We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures.  ...  Numerical results show that our algorithms can perform well even for very large instances of primal block angular convex QP problems.  ...  Acknowledgements We would like to thank Professor Jordi Castro for sharing with us his solver BlockIP so that we are able to evaluate the performance of our algorithm more comprehensively.  ... 
arXiv:1812.04941v1 fatcat:jjah6n7onrd6xihrzr7pvrofua

Page 4531 of Mathematical Reviews Vol. , Issue 2002F [page]

2002 Mathematical Reviews  
A. (D-HDBG-SC; Heidelberg) ; Kostyukova, O. I. (BE-AOS; Minsk) An algorithm for solving convex quadratic programming problems with linear equality and inequality constraints. (Russian.  ...  An algorithm for solving convex quadratic programs with linear constraints is presented. The method combines the steepest descent method with the active set strategy.  ... 

Solving variational inequalities with a quadratic cut method: a primal-dual, Jacobian-free approach

Michel Denault, J.-L. Goffin
2004 Computers & Operations Research  
First, we deÿne a primal-dual method to ÿnd the analytic center at each iteration.  ...  We extend in two directions the Analytic Center, Cutting Plane Method for Variational Inequalities with quadratic cuts, ACCPM-VI(quadratic cuts), introduced by Denault and Go n in 1998.  ...  In the next section, we discuss a primal-dual, heuristic approach to solve this problem.  ... 
doi:10.1016/s0305-0548(03)00032-7 fatcat:kjvtacxq6jejxb2s6qlbzh5psm

Warmstarting the homogeneous and self-dual interior point method for linear and conic quadratic problems

Anders Skajaa, Erling D. Andersen, Yinyu Ye
2012 Mathematical Programming Computation  
We present two strategies for warmstarting primal-dual interior point methods for the homogeneous self-dual model when applied to mixed linear and quadratic conic optimization problems.  ...  This is a major advantage when comparing to previously suggested strategies that require a pool of iterates from the solution process of the initial problem.  ...  Symmetric Primal-Dual Interior Point Algorithm To carry out numerical experiments, we have implemented in Matlab a symmetric primal-dual interior point method called ccopt.  ... 
doi:10.1007/s12532-012-0046-z fatcat:6jx7xjdpejhobm4ijbarc5ywwa
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