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Global optimization of Optimal Power Flow using a branch & bound algorithm

Ajit Gopalakrishnan, Arvind U. Raghunathan, Daniel Nikovski, Lorenz T. Biegler
2012 2012 50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality.  ...  Abstract-We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality.  ...  The Lagrangian dual based algorithm was unable to close the gap due to computational difficulties in solving the non-smooth dual relaxation through a subgradient method.  ... 
doi:10.1109/allerton.2012.6483274 dblp:conf/allerton/GopalakrishnanRNB12 fatcat:5qku2jn4ivgnrprfncv2zresda

Constraint-based watermarking techniques for design IP protection

A.B. Kahng, J. Lach, W.H. Mangione-Smith, S. Mantik, I.L. Markov, M. Potkonjak, P. Tucker, H. Wang, G. Wolfe
2001 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
When minimizing a given objective function is challenging because of, for example, combinatorial complexity or points of nondi erentiability, one can apply more e cient and easier-to-implement algorithms  ...  In this paper, we a p p r o ximate convex non-smooth continuous functions by convex di erentiable functions which are parameterized by a scalar 0 and have c o n venient limit behavior as ! 0.  ...  For example, in pure min-cut placemet which cannot directly address non-linear terms, competitive runtimes for a circuit with 20K cells will be on the order of 10-20 seconds per start 2-4 independent randomized  ... 
doi:10.1109/43.952740 fatcat:l22bt26shvbrfkw4shw7p2biai

Efficient optimization by modifying the objective function: applications to timing-driven VLSI layout

R. Baldick, A.B. Kahng, A. Kennings, I.L. Markov
2001 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
When minimizing a given objective function is challenging because of, for example, combinatorial complexity or points of nondi erentiability, one can apply more e cient and easier-to-implement algorithms  ...  In this paper, we a p p r o ximate convex non-smooth continuous functions by convex di erentiable functions which are parameterized by a scalar 0 and have c o n venient limit behavior as ! 0.  ...  For example, in pure min-cut placemet which cannot directly address non-linear terms, competitive runtimes for a circuit with 20K cells will be on the order of 10-20 seconds per start 2-4 independent randomized  ... 
doi:10.1109/81.940185 fatcat:fe3hcuuhozgprlnqch7enlsexu

Neural Network for Nonsmooth, Nonconvex Constrained Minimization Via Smooth Approximation

Wei Bian, Xiaojun Chen
2014 IEEE Transactions on Neural Networks and Learning Systems  
A neural network based on smoothing approximation is presented for a class of nonsmooth, nonconvex constrained optimization problems, where the objective function is nonsmooth and nonconvex, the equality  ...  This approach can find a Clarke stationary point of the optimization problem by following a continuous path defined by a solution of an ordinary differential equation.  ...  presentation of the results in this paper.  ... 
doi:10.1109/tnnls.2013.2278427 pmid:24807450 fatcat:zcgf6rltbvdtrk45lwapmbjg6q

Optimizing revenue for bandwidth auctions over networks with time reservations

Pablo Belzarena, Fernando Paganini, Andrés Ferragut
2011 Computer Networks  
to obtain a convergent algorithm.  ...  This paper concerns the problem of allocating network capacity through periodic auctions, in which users submit bids for fixed amounts of end-to-end service.  ...  The linear term with κ s > 0 makes it possible to have an intersecting point a s which is not an integer multiple of σ s , as required for solving the relaxed problem.  ... 
doi:10.1016/j.comnet.2011.03.009 fatcat:eec3tfvxyfeolh2bqvirzey434

Prioritized Flow Optimization With Multi-Path and Network Coding Based Routing for Scalable Multirate Multicasting

Junni Zou, Hongkai Xiong, Chenglin Li, Li Song, Zhihai He, Tsuhan Chen
2011 IEEE transactions on circuits and systems for video technology (Print)  
Based on primal decomposition and primal-dual analysis, we develop a decentralized algorithm with two optimization levels to solve the performance optimization problem.  ...  Content priority of video coding layers is considered during the flow routing to determine the optimal multicast paths and associated data rates for each layer.  ...  of P2a and denoted by (9)-(11). 1) Subgradient Optimization: Now we study the convergence of the subgradient algorithm applied in the highlevel optimization.  ... 
doi:10.1109/tcsvt.2010.2077576 fatcat:smpu3sh5f5dydc3o2aefjsgu7y

Provably Correct Automatic Subdifferentiation for Qualified Programs [article]

Sham Kakade, Jason D. Lee
2019 arXiv   pre-print
the function itself --- is of central importance in optimization; it allows us to quickly obtain (high dimensional) gradients of scalar loss functions which are subsequently used in black box gradient-based  ...  optimization procedures.  ...  Lee acknowledges support of the ARO under MURI Award W911NF-11-1-0303. This is part of the collaboration  ... 
arXiv:1809.08530v2 fatcat:tquagy5e6jeshjb3jravcwbxoi

Optimization Algorithms as Robust Feedback Controllers [article]

Adrian Hauswirth, Saverio Bolognani, Gabriela Hug, Florian Dörfler
2021 arXiv   pre-print
However, our focus lies on recent methods under the name of "feedback-based optimization".  ...  Mathematical optimization is one of the cornerstones of modern engineering research and practice.  ...  Acknowledgements The research leading to these results was supported by ETH Zürich funds and by the Swiss Federal Office of Energy grant #SI/501708 UNICORN.  ... 
arXiv:2103.11329v1 fatcat:awpupmsxirdw5lnbsvmkhrs57a

Generalized Optimization: A First Step Towards Category Theoretic Learning Theory [article]

Dan Shiebler
2021 arXiv   pre-print
We use this operator to generalize several optimization algorithms, including a straightforward generalization of gradient descent and a novel generalization of Newton's method.  ...  We then explore which properties of these algorithms are preserved in this generalized setting.  ...  We believe that this line of research will accelerate future machine learning research by helping researchers better understand the foundational components of the algorithms that they use.  ... 
arXiv:2109.10262v1 fatcat:onman4tzgbckznt72nzaasqmyu

LCD Motion Blur: Modeling, Analysis, and Algorithm

Stanley H. Chan, Truong Q. Nguyen
2011 IEEE Transactions on Image Processing  
Liquid crystal display (LCD) devices are well known for their slow responses due to the physical limitations of liquid crystals.  ...  , which are two state-of-the-art LCD deblurring algorithms.  ...  Algorithm 2 shows the pseudocode for our projected subgradient algorithm using the Armijo line search. Algorithm 2 Subgradient Projection Algorithm Set and (Typically, ). Set initial step size .  ... 
doi:10.1109/tip.2011.2109728 pmid:21292596 fatcat:ctya55ci75cptmdj6ipfvbxkny

A survey of computational approaches to three-dimensional layout problems

J. Cagan, K. Shimada, S. Yin
2002 Computer-Aided Design  
algorithm exploratory moves evaluations / simulations decision making accept, reject moves stop criteria topological connections attachment points route definition constraints non-overlap proximity alignment  ...  Major constituent parts for generic layout synthesis. Optimization, 7(1):1-25.  ...  Multiple runs from different starting points may be necessary because of the fractalness of the layout space.  ... 
doi:10.1016/s0010-4485(01)00109-9 fatcat:henmqhb6dbeudijlybfddxnki4

Near-Optimal Lower Bounds For Convex Optimization For All Orders of Smoothness [article]

Ankit Garg, Robin Kothari, Praneeth Netrapalli, Suhail Sherif
2021 arXiv   pre-print
We study the complexity of optimizing highly smooth convex functions.  ...  This is known to be optimal (up to log factors) for deterministic algorithms, but known lower bounds for randomized algorithms do not match this bound.  ...  Towards this let x be any point in B β (x). Let I x be the set {i ∈ [k]|h(x ) = f i (x )}. The set of subgradients of the non-smooth term at x is the convex hull of {∇(f i − f j )(x )} i∈I(x ) .  ... 
arXiv:2112.01118v1 fatcat:cgv6ckc7mjgahbkqwj3efgrqvy

The Multiplicative Weights Update Method: a Meta-Algorithm and Applications

Sanjeev Arora, Elad Hazan, Satyen Kale
2012 Theory of Computing  
Other applications of the multiplicative weights algorithm in computational geometry include Clarkson's algorithm for linear programming with a bounded number of variables in linear time [20, 21] .  ...  Garg and Khandekar [28] describe a common framework for convex optimization problems that contains Garg-Könemann and Plotkin-Shmoys-Tardos as subcases.  ...  In addition, since a preprint of this paper was available on the Internet for several years prior to publication, a number of people have read it and suggested improvements; we cannot list them all but  ... 
doi:10.4086/toc.2012.v008a006 dblp:journals/toc/AroraHK12 fatcat:hbikmeaflraqhgxl2pectrb2bq

Optimal robust path planning in general environments

T.C. Hu, A.B. Kahng, G. Robins
1993 IEEE Transactions on Robotics and Automation  
Acknowledgements We are grateful to Professors Sheila Greibach and John Canny, a s w ell as the anonymous referees, for providing helpful comments on previous versions of this paper.  ...  of multiple wires in a printed circuit board, etc.  ...  Starting with an empty o w, the Dinic algorithm iteratively augments the ow in stages; the optimal ow solution is achieved when no ow augmentation is possible.  ... 
doi:10.1109/70.265921 fatcat:nvjwjovqmnedddhezxrooic7ya

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  A v ariation of bundle methods is presented by means of which such a t ype of problems can be solved.In this variation a dynamic polyhedral model of dom is generated by means of normal vectors.In addition  ...  To nd this subset, we propose an algorithm based on an interior point technique for nonlinear optimization.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa
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