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Random Conic Pursuit for Semidefinite Programming
2010
Neural Information Processing Systems
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We present a novel algorithm, Random Conic Pursuit, that solves semidefinite programs (SDPs) via repeated optimization over randomly selected two-dimensional subcones of the PSD cone. ...
This property renders Random Conic Pursuit of particular interest for machine learning applications, in which the relevant SDPs are generally based upon random data and so exact minima are often not a ...
Acknowledgments We are grateful to Guillaume Obozinski for early discussions that motivated this line of work. ...
dblp:conf/nips/KleinerRJ10
fatcat:oidm3var4zh4das7asyivyc3ka
BILGO: Bilateral greedy optimization for large scale semidefinite programming
2014
Neurocomputing
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To enable the application of these tasks on a large-scale, scalability and computational efficiency are considered desirable properties for a practical semidefinite programming algorithm. ...
Many machine learning tasks (e.g. metric and manifold learning problems) can be formulated as convex semidefinite programs. ...
Zhenjie Zhang for his helpful discussions and suggestions on this paper. Hao and Yuan are supported by NSF-China (61070033, 61100148), NSF-Guangdong (9251009001000005, S2011040004804). ...
doi:10.1016/j.neucom.2013.07.024
fatcat:vw6tiehxljanvgdkzlps7i4wuy
Conic Geometric Programming
[article]
2013
arXiv
pre-print
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We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). ...
The conic constraints are the central feature of conic programs such as SDPs, while upper bounds on combined exponential/affine functions are generalizations of the types of constraints found in GPs. ...
Acknowledgements The authors would like to thank Pablo Parrilo for many enlightening conversations, and Leonard Schulman for pointers to the literature on Von-Neumann entropy. ...
arXiv:1310.0899v2
fatcat:mtx77cfgsvcqvpsmbiwcubhmdy
Conic geometric programming
2014
2014 48th Annual Conference on Information Sciences and Systems (CISS)
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We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). ...
The conic constraints are the central feature of conic programs such as SDPs, while upper bounds on combined exponential/affine functions are generalizations of the types of constraints found in GPs. ...
Acknowledgements The authors would like to thank Pablo Parrilo for many enlightening conversations, and Leonard Schulman for pointers to the literature on Von-Neumann entropy. ...
doi:10.1109/ciss.2014.6814151
dblp:conf/ciss/ChandrasekaranS14
fatcat:7jzbkvnpkbfhjgtfwlgbhunw6i
Iterative Inner/outer Approximations for Scalable Semidefinite Programs using Block Factor-width-two Matrices
[article]
2022
arXiv
pre-print
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In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). ...
Our inner/outer approximating algorithms generate a sequence of upper/lower bounds of increasing accuracy for the optimal SDP cost. ...
INTRODUCTION Semidefinite programs (SDPs) are a class of convex optimization problems over the positive semidefinite (PSD) cone. ...
arXiv:2204.06759v2
fatcat:mipqjomgmffftc5yp6ayvjqqze
Feasible Point Pursuit and Successive Approximation of Non-Convex QCQPs
2015
IEEE Signal Processing Letters
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In this paper, a new feasible point pursuit successive convex approximation (FPP-SCA) algorithm is proposed for non-convex QCQPs. ...
Quadratically constrained quadratic programs (QCQPs) have a wide range of applications in signal processing and wireless communications. Non-convex QCQPs are NP-hard in general. ...
To solve the SDR and the SCA , the modeling language YALMIP [19] is used and the generic conic programming solver SeDuMi [20] is chosen as the I RESULTS USING THE SDR APPROACH FOR TABLE II RESULTS ...
doi:10.1109/lsp.2014.2370033
fatcat:jgb6v3q2vrb7habhlswg5z66va
Decomposed Structured Subsets for Semidefinite and Sum-of-Squares Optimization
[article]
2021
arXiv
pre-print
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Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. ...
An existing basis pursuit method is adapted into this framework to iteratively refine bounds. ...
Preliminaries for Polynomial Optimization A polynomial optimization problem may be approximated by semidefinite programming. ...
arXiv:1911.12859v4
fatcat:nortxjtqbnfizjcof7rdyyrtxe
Improving Efficiency and Scalability of Sum of Squares Optimization: Recent Advances and Limitations
[article]
2017
arXiv
pre-print
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It is well-known that any sum of squares (SOS) program can be cast as a semidefinite program (SDP) of a particular structure and that therein lies the computational bottleneck for SOS programs, as the ...
The second method bypasses semidefinite programming altogether and relies instead on solving a sequence of more tractable convex programs, namely linear and second order cone programs. ...
semidefinite) program. ...
arXiv:1710.01358v1
fatcat:pnqyg5iayjh6bpsm44sgd2t3se
Exploiting Sparsity in the Coefficient Matching Conditions in Sum-of-Squares Programming Using ADMM
2017
IEEE Control Systems Letters
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This paper introduces an efficient first-order method based on the alternating direction method of multipliers (ADMM) to solve semidefinite programs (SDPs) arising from sum-of-squares (SOS) programming ...
Each iteration of our algorithm requires one projection onto the positive semidefinite cone and the solution of multiple quadratic programs with closed-form solutions free of any matrix inversion. ...
NUMERICAL EXPERIMENTS We implemented our techniques in SOSADMM, an opensource first-order MATLAB solver for conic programs with row sparsity. ...
doi:10.1109/lcsys.2017.2706941
fatcat:rvuj5xprr5cenefcmmpu5rapsa
Conditions for existence of dual certificates in rank-one semidefinite problems
2014
Communications in Mathematical Sciences
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Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. ...
The important message of this paper is that dual certificates may not exist for semidefinite programs that involve orthogonal measurements with respect to positive-semidefinite matrices. ...
not hold) for semidefinite programs. ...
doi:10.4310/cms.2014.v12.n7.a11
fatcat:moaebara4vdfpddzxz3fkp2k5a
Terracini Convexity
[article]
2022
arXiv
pre-print
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Our approach is more flexible and includes, for example, the cone of positive-semidefinite matrices as a special case (this cone is not neighborly in general). ...
As a demonstration of the utility of our framework in the non-polyhedral case, we give a characterization based on Terracini convexity of the tightness of semidefinite relaxations for certain inverse problems ...
Acknowledgements The authors would like to thank Rainer Sinn for helpful conversations. ...
arXiv:2010.00805v2
fatcat:kshfa5y6onb67mwmykr5qbmerm
Fast ADMM for sum-of-squares programs using partial orthogonality
[article]
2018
arXiv
pre-print
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Precisely, we show how a "diagonal plus low rank" structure implied by partial orthogonality can be exploited to project efficiently the iterates of a recent ADMM algorithm for generic conic programs onto ...
When sum-of-squares (SOS) programs are recast as semidefinite programs (SDPs) using the standard monomial basis, the constraint matrices in the SDP possess a structural property that we call partial orthogonality ...
In fact, checking for the existence (or lack) of an SOS representation amounts to solving a semidefinite program (SDP) [3] . ...
arXiv:1708.04174v2
fatcat:vo3wdn56n5g3zbd3fczndtw3qy
Optimal designs for rational function regression
[article]
2011
arXiv
pre-print
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After discussing linear models, applications for finding locally optimal designs for nonlinear regression models involving rational functions are presented, then extensions to robust regression designs ...
The method is of considerable practical importance, with the potential for instance to impact design software development. ...
We solved the resulting semidefinite program for the degree 20 model; the computation required 0.4 seconds. ...
arXiv:1009.1444v2
fatcat:fzkcp6npwrh6bmbunu6xnsfsii
Optimal Designs for Rational Function Regression
2012
Journal of the American Statistical Association
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Our main result is a characterization of the support of the D-, E-, A-, and Φ poptimal designs as the optimal solutions of a semidefinite optimization problem. ...
Similar characterizations are known for A-and E-optimal designs for polynomial regression, see, for example the classic monographs [14, 33] . ...
We solved the resulting semidefinite program for the degree 20 model; the computation required 0.4 seconds. ...
doi:10.1080/01621459.2012.656035
fatcat:t7i3nmgedraslpjd6ebvyqxrma
Optimization of Convex Functions with Random Pursuit
2013
SIAM Journal on Optimization
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We also present an accelerated heuristic version of the Random Pursuit algorithm which significantly improves standard Random Pursuit on all numerical benchmark problems. ...
To support the theoretical results we present extensive numerical performance results of Random Pursuit, two gradient-free algorithms recently proposed by Nesterov, and a classical adaptive step-size random ...
Acknowledgments We sincerely thank Martin Jaggi for several helpful discussions.
RANDOM PURSUIT ...
doi:10.1137/110853613
fatcat:od2xxkrnefhrzbm4byjj3lqoza
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