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Semidefinite Relaxation for Two Mixed Binary Quadratically Constrained Quadratic Programs: Algorithms and Approximation Bounds [article]

Zi Xu, Mingyi Hong
2014 arXiv   pre-print
This paper develops new semidefinite programming (SDP) relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation performance  ...  The second class of problem finds a series of minimum norm vectors subject to a set of quadratic constraints and a cardinality constraint with both binary and continuous variables.  ...  Acknowledgments This research is supported by the Chinese NSF under the grant 11101261 and the First-class Discipline of Universities in Shanghai.  ... 
arXiv:1403.3998v1 fatcat:zuiodtvlgjhkrp6za5iq435wc4

Efficient Semidefinite Programming with approximate ADMM [article]

Nikitas Rontsis and Paul J. Goulart and Yuji Nakatsukasa
2021 arXiv   pre-print
simply by projecting approximately to the Semidefinite cone.  ...  Tenfold improvements in computation speed can be brought to the alternating direction method of multipliers (ADMM) for Semidefinite Programming with virtually no decrease in robustness and provable convergence  ...  Exploiting Low- Rank Structure in Semidefinite Programming by Approximate Opera- tor Splitting. arXiv 1810.05231, 2018. A Stathopoulos and J. R. McCombs.  ... 
arXiv:1912.02767v2 fatcat:nxvv6nc6obffbhxwd45ej6b4we

Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs [chapter]

Eran Halperin, Uri Zwick
1999 Lecture Notes in Computer Science  
We present a semide nite programming relaxation of MAX 4-SAT and a new family of rounding procedures that try to cope well with clauses of various sizes.  ...  Karlo and Zwick obtained recently an optimal 7=8-approximation algorithm for MAX 3-SAT.  ...  We end this section with a short survey of related results. The 7=8-approximation algorithm for MAX 3-SAT is based on the MAX CUT approximation algorithm of Goemans and Williamson 12] .  ... 
doi:10.1007/3-540-48777-8_16 fatcat:cnqiu5eccrfftbke66q2iinhu4

Copositive Programming – a Survey [chapter]

Mirjam Dür
2010 Recent Advances in Optimization and its Applications in Engineering  
, including modeling issues and applications, the connection to semidefinite programming and sum-of-squares approaches, as well as algorithmic solution approaches for copositive programs.  ...  It can be seen as a generalization of semidefinite programming, since it means optimizing over the cone of so called copositive matrices.  ...  Algorithms The approximation hierarchies described in the last section can be used to approximate a copositive program, and in many settings this gives very good results and strong bounds.  ... 
doi:10.1007/978-3-642-12598-0_1 fatcat:ys5hz2zqafe5dpkvj7ladt3wdu

Some recent developments in nonlinear optimization algorithms

A. Sartenaer, J.P. Penot
2003 ESAIM: Proceedings and Surveys  
in nonlinear optimization algorithms and to practical solvers and their performance.  ...  We then focus on constrained optimization and give the main ideas of two classes of methods, the Sequential Quadratic Programming (SQP) methods and the interior-point methods.  ...  Acknowledgments We are grateful to Caroline Sainvitu for her careful reading of the manuscript and several suggestions that improved the presentation, and to anonymous referees for their constructive comments  ... 
doi:10.1051/proc:2003006 fatcat:qwbrklidqjhq7dpufvn2njbsfi

A Survey of Recent Advances in Hierarchical Clustering Algorithms

F. Murtagh
1983 Computer journal  
This 'progress report' details new algorithmic approaches in this area, and reviews recent results.  ...  A general framework for hierarchical, agglomerative clustering algorithms is discussed here, which opens up the prospect of much improvement on current, widely-used algorithms.  ...  It was briefly surveyed by Bock (Ref. 35, , and by Rohlf. 20 However it has in particular emerged as a basis for general clustering algorithms in a series of articles in the journal Les Cahiers de /  ... 
doi:10.1093/comjnl/26.4.354 fatcat:kqnykk4jarhmragotjj7nmeysa

A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization [article]

Songbai Liu
2022 arXiv   pre-print
In this paper, we begin with a taxonomy of scalable MOPs and learnable MOEAs, followed by an analysis of the challenges that scaling up MOPs pose to traditional MOEAs.  ...  Recent decades have witnessed remarkable advancements in multiobjective evolutionary algorithms (MOEAs) that have been adopted to solve various multiobjective optimization problems (MOPs).  ...  In particular, A Survey on Learnable Evolutionary Algorithms for Scalable Multiobjective Optimization Songbai Liu E the agent (like a generator) based on the observation of state and reward to create  ... 
arXiv:2206.11526v1 fatcat:mlgcvsi4sfadflm3xxfkbfjk6q

A Survey of Manifold-Based Learning Methods [chapter]

Xiaoming Huo, Xuelei (Sherry) Ni, Andrew K. Smith
2008 Recent Advances in Data Mining of Enterprise Data: Algorithms and Applications  
We review the ideas, algorithms, and numerical performance of manifold-based machine learning and dimension reduction methods.  ...  This chapter is based on an invited survey presentation that was delivered by Huo at the 2004 INFORMS Annual Meeting, which was held in Denver, CO, USA.  ...  survey.  ... 
doi:10.1142/9789812779861_0015 fatcat:imart6ri7nce3nxhtvcqgez4ci

A Survey of Recent Scalability Improvements for Semidefinite Programming with Applications in Machine Learning, Control, and Robotics [article]

Anirudha Majumdar, Georgina Hall, Amir Ali Ahmadi
2019 arXiv   pre-print
approximate solutions to semidefinite programs, (iii) more scalable algorithms that rely on augmented Lagrangian techniques and the alternating direction method of multipliers, and (iv) approaches that  ...  trade off scalability with conservatism (e.g., by approximating semidefinite programs with linear and second-order cone programs).  ...  University, the Sloan Fellowship, the MURI Award of the AFOSR, the Office of Naval Research [Award Number: N00014-18-1-2873], the NSF CRII award [IIS-1755038], and the Amazon Research Award.  ... 
arXiv:1908.05209v3 fatcat:g2vqfhv27vgddbv7l4xciywf4u

The quadratic knapsack problem—a survey

David Pisinger
2007 Discrete Applied Mathematics  
A short overview of heuristics, reduction techniques, branch-and-bound algorithms and approximation results is given, followed by an overview of valid inequalities for the quadratic knapsack polytope.  ...  Techniques for deriving the bounds include relaxation from upper planes, linearization, reformulation, Lagrangian relaxation, Lagrangian decomposition, and semidefinite programming.  ...  Acknowledgments The author would like to thank Jarl Friis for valuable comments during the writing of this paper-in particular with the section on semidefinite programming, and Anders Bo Rasmussen and  ... 
doi:10.1016/j.dam.2006.08.007 fatcat:jshopbokirfdfiackwmzdawgwq

A Survey of Relaxations and Approximations of the Power Flow Equations

Daniel K. Molzahn, Ian A. Hiskens
2019 Foundations and Trends® in Electric Energy Systems  
Borchers, "CSDP, A C Library for Semidefinite Programming," OptimizationMethods and Software, vol. 11, no. 1-4, pp. 613-623, 1999. [139] T. Gally, M. E. Pfetsch, and S.  ...  Kirschen, and B. Zhang, "Accurate Semidefinite Programming Models for Optimal Power Flow in Distribution Systems," arXiv:1711.07853, December 2017. [147] R. A.  ... 
doi:10.1561/3100000012 fatcat:nabqi7umufexxacy32zbbhg53a

A Survey of ADMM Variants for Distributed Optimization: Problems, Algorithms and Features [article]

Yu Yang, Xiaohong Guan, Qing-Shan Jia, Liang Yu, Bolun Xu, Costas J. Spanos
2022 arXiv   pre-print
However, there lacks a survey to document those developments and discern the results. To achieve such a goal, this paper provides a comprehensive survey on ADMM variants.  ...  This survey is expected to work as a tutorial for both developing distributed optimization in broad areas and identifying existing theoretical research gaps.  ...  As a result, the method is applicable to more general applications, such as sparsity regression [107] and integer programming [68] .  ... 
arXiv:2208.03700v1 fatcat:typcmi5hh5hqdftprifgaptpnq

Wireless Networks with RF Energy Harvesting: A Contemporary Survey [article]

Xiao Lu, Ping Wang, Dusit Niyato, Dong In Kim, Zhu Han
2014 arXiv   pre-print
First, we present an overview of the RF-EHNs including system architecture, RF energy harvesting techniques and existing applications.  ...  Radio frequency (RF) energy transfer and harvesting techniques have recently become alternative methods to power the next generation wireless networks.  ...  By applying semidefinite relaxation, the original problem is then transformed into a convex semidefinite program and it can be solved efficiently.  ... 
arXiv:1406.6470v6 fatcat:bjmvi4hwfnhvbnodubqipsdija

Randomization in Graph Optimization Problems: A Survey [chapter]

David R. Karger
2001 Handbook of Randomized Computing  
Semidefinite Programming (M. Ramana, P.  ...  Pardalos) Semidefinite programming is a generalization of linear programming in which the nonnegative vector of decision variables is replaced by a square positive semidefinite matrix of such variables  ...  transformations, and (iii) a potential function to measure the progress of the algorithm.  ... 
doi:10.1007/978-1-4615-0013-1_4 fatcat:cmncmhkagrgrhpmf6be3nztgwq

Robust optimization – A comprehensive survey

Hans-Georg Beyer, Bernhard Sendhoff
2007 Computer Methods in Applied Mechanics and Engineering  
methods such as stochastic approximation and evolutionary computation.  ...  Starting with a short glimps of Taguchi's robust design methodology, a detailed survey of approaches to robust optimization is presented.  ...  In [92] the robust design of a truss has been modeled by a nonlinear semidefinite programming problem which has been solved by a sequence of semidefinite programs obtained by successive linearization  ... 
doi:10.1016/j.cma.2007.03.003 fatcat:dldw7fpiurekrafv7yexyv5s4y
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