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An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints [article]

Elisabete Alberdi, Mikel Antoñana, Joseba Makazaga, Ander Murua
2019 arXiv   pre-print
We present an algorithm based on continuation techniques that can be applied to solve numerically minimization problems with equality constraints.  ...  Such systems arise, for instance, in the context of the construction of high order optimized differential equation solvers.  ...  A variety of local minimization methods for minimization problems with non-linear equality constrains are available.  ... 
arXiv:1909.07263v1 fatcat:zw74y2mstrespklrkydy64swxu

Order constraints for single machine scheduling with non-linear cost [chapter]

Christoph Dürr, Oscar C. Vásquez
2013 2014 Proceedings of the Sixteenth Workshop on Algorithm Engineering and Experiments (ALENEX)  
In this paper we consider the non-linear objective function wjC β j , where Cj is the completion time of job j and β > 0 is some arbitrary real constant.  ...  Except for β = 1 the complexity status of this problem is open. Past research mainly focused on the quadratic case (β = 2) and proposed different techniques to speed up exact algorithms.  ...  constraints.  ... 
doi:10.1137/1.9781611973198.10 dblp:conf/alenex/DurrV14 fatcat:eqiprmzjwfhznb2275buarhara

Interlaced Greedy Algorithm for Maximization of Submodular Functions in Nearly Linear Time [article]

Alan Kuhnle
2019 arXiv   pre-print
A deterministic approximation algorithm is presented for the maximization of non-monotone submodular functions over a ground set of size n subject to cardinality constraint k; the algorithm is based upon  ...  time complexity of the previously fastest deterministic algorithm for this problem.  ...  Their algorithm also works under a more general constraint than cardinality constraint; namely, a matroid constraint. This algorithm is the latest in a series of works (e.g.  ... 
arXiv:1902.06179v3 fatcat:fmekwvbm6fbpnkscy5vg6yiz5y

A fast branch-and-bound algorithm for non-convex quadratic integer optimization subject to linear constraints using ellipsoidal relaxations

Christoph Buchheim, Marianna De Santis, Laura Palagi
2015 Operations Research Letters  
We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set.  ...  In the first approach, we intersect the ellipsoids with the feasible linear subspace. In the second approach we penalize exactly the linear constraints.  ...  Introduction We address quadratic integer optimization problems with box constraints and linear equality constraints, min q(x) = x Qx + c x s.t.  ... 
doi:10.1016/j.orl.2015.05.001 fatcat:jfkzu4nr6vayzeccxnpej43odu

Extending Linear Relaxation for User Interface Layout

N. Jamil, J. Mueller, C. Lutteroth, G. Weber
2012 2012 IEEE 24th International Conference on Tools with Artificial Intelligence  
Furthermore, we propose two algorithms for solving specifications containing soft constraints: constraint insertion and constraint removal.  ...  In this paper we extend linear relaxation to non-square matrices and soft constraints, and identify pivot assignment as the major issue to overcome in this process.  ...  We propose two algorithms for solving systems of prioritized linear constraints with the linear relaxation method.  ... 
doi:10.1109/ictai.2012.132 dblp:conf/ictai/JamilMLW12 fatcat:pwfuxmzby5gxxoy7lktiothzbi

Extending linear relaxation for non-square matrices and soft constraints

Noreen Jamil, Johannes Müller, M. Asif Naeem, Christof Lutteroth, Gerald Weber
2016 Journal of Computational and Applied Mathematics  
With these algorithms, it is possible to prioritize constraints: if there are conflicting constraints in a specification, as it is commonly the case for UI layout, only the constraints with lower priority  ...  Furthermore, we propose three algorithms for solving specifications containing soft constraints: prioritized IIS detection, prioritized deletion filtering and prioritized grouping constraints.  ...  In Section 5 we propose three conflict resolution algorithms for solving systems of prioritized linear constraints with the linear relaxation method.  ... 
doi:10.1016/j.cam.2016.05.006 fatcat:4k6byy6ogzghzi4u6ccxne3n3q

Dynamic approximation of complex graphical constraints by linear constraints

Nathan Hurst, Kim Marriott, Peter Moulder
2002 Proceedings of the 15th annual ACM symposium on User interface software and technology - UIST '02  
Current constraint solving techniques for interactive graphical applications cannot satisfactorily handle constraints such as non-overlap, or containment within non-convex shapes or shapes with smooth  ...  We present a generic new technique for efficiently handling such kinds of constraints based on trust regions and linear arithmetic constraint solving.  ...  The first is a generic algorithm for solving complex non-linear constraints by dynamically approximating the constraints with linear constraints.  ... 
doi:10.1145/571985.572012 dblp:conf/uist/HurstMM02 fatcat:bteqsrgi45dzvfenraae55gtt4

Dynamic approximation of complex graphical constraints by linear constraints

Nathan Hurst, Kim Marriott, Peter Moulder
2002 Proceedings of the 15th annual ACM symposium on User interface software and technology - UIST '02  
Current constraint solving techniques for interactive graphical applications cannot satisfactorily handle constraints such as non-overlap, or containment within non-convex shapes or shapes with smooth  ...  We present a generic new technique for efficiently handling such kinds of constraints based on trust regions and linear arithmetic constraint solving.  ...  The first is a generic algorithm for solving complex non-linear constraints by dynamically approximating the constraints with linear constraints.  ... 
doi:10.1145/572010.572012 fatcat:ja7hhgwfgbarvcq4vuka2okgui

Leaders and followers algorithm for constrained non-linear optimization

Helen Yuliana Angmalisang, Syaiful Anam, Sobri Abusini
2019 Indonesian Journal of Electrical Engineering and Computer Science  
In this paper, Leaders and Followers was modified for constrained non-linear optimization.  ...  Moreover, the proposed algorithm had difficulty in solving high dimensional optimization problem with non-linear constraints and any problem which has more than one equality constraint.  ...  Constrained non-linear optimization is defined as a constrained optimization problem where its objective function or at least one of the constraints is non-linear function [3] .  ... 
doi:10.11591/ijeecs.v13.i1.pp162-169 fatcat:aibpg6jjo5bztbm6sc72y2drdi

Solving complex path conditions through heuristic search on induced polytopes

Peter Dinges, Gul Agha
2014 Proceedings of the 22nd ACM SIGSOFT International Symposium on Foundations of Software Engineering - FSE 2014  
We show how a simple combination of linear constraint solving and heuristic search can overcome these limitations. We call this technique Concolic Walk.  ...  Furthermore, our algorithm improves the coverage of two state-of-the-art test generators by 21% and 32%.  ...  The authors would like to thank Mohsen Vakilian and Tao Xie for insightful comments on early drafts of this paper.  ... 
doi:10.1145/2635868.2635889 dblp:conf/sigsoft/DingesA14 fatcat:wvzuyxstbjck5mtggcfjsbiony

Solving Sparse Linear Constraints [chapter]

Shuvendu K. Lahiri, Madanlal Musuvathi
2006 Lecture Notes in Computer Science  
Sparse linear arithmetic (SLA) denotes a set of linear arithmetic constraints with a very few non-difference constraints.  ...  For SLA constraints, the space and time complexity of the resulting algorithm is dominated solely by the complexity for solving the difference constraints.  ...  for non-difference constraints).  ... 
doi:10.1007/11814771_39 fatcat:swbnniy7lfch5puet7feom6r44

Disjunction of Non-binary and Numeric Constraint Satisfaction Problems [chapter]

Miguel A. Salido, Federico Barber
2002 Lecture Notes in Computer Science  
Furthermore, a Constraint Ordering Algorithm (COA) classifies the resultant constraints from the most restricted to the least restricted one.  ...  In this paper, we propose an algorithm called DHSA that solves numeric non-binary CSPs with disjunctions in a natural way, as non-binary disjunctive CSP solver.  ...  In this paper, we propose an algorithm for solving problems with numeric non-binary disjunctive constraints.  ... 
doi:10.1007/3-540-36079-4_14 fatcat:hgs3n6m7fbc7tdq274vuagdazq

Solving Disjunctive Constraints for Interactive Graphical Applications [chapter]

Kim Marriott, Peter Moulder, Peter J. Stuckey, Alan Borning
2001 Lecture Notes in Computer Science  
We give both a generic algorithm, and a version specialised for linear arithmetic constraints that makes use of the Cassowary constraint solving algorithm.  ...  The key insight behind our algorithms is that the disjuncts in a non-overlap constraint are not disjoint: during direct manipulation we need only move between disjuncts that are adjacent in the sense that  ...  We thank Nathan Hurst for his insightful comments and criticisms.  ... 
doi:10.1007/3-540-45578-7_25 fatcat:u6uwragthvappbcswnimkvoy3y

Computational Study of Non-linear Great Deluge for University Course Timetabling [chapter]

Joe Henry Obit, Dario Landa-Silva
2010 Studies in Computational Intelligence  
For this study, we apply the non-linear great deluge algorithm to difficult instances of the university course timetabling problem.  ...  In this paper, we conduct a computational study of a modified version of the great deluge algorithm in which the decay rate of the water level is non-linear.  ...  Fig. 2 Fig. 3 23 Detailed comparison of non-linear great deluge against other algorithms for small instances fromTable 1Detailed comparison of non-linear great deluge against other algorithms for medium  ... 
doi:10.1007/978-3-642-13428-9_14 fatcat:psl2x2oj4fdathgiemkjpvppry

On Applying Cutting Planes in DLL-Based Algorithms for Pseudo-Boolean Optimization [chapter]

Vasco Manquinho, João Marques-Silva
2005 Lecture Notes in Computer Science  
Moreover, we also establish conditions that enable clause learning and non-chronological backtracking in the presence of conflicts involving constraints generated by cutting plane techniques.  ...  This paper proposes the utilization of cutting planes in a DLL-style PBO algorithm, which incorporates the most effective techniques for PBO.  ...  Furthermore, we show that these new constraints can be used for performing non-chronological backtracking.  ... 
doi:10.1007/11499107_38 fatcat:khliq42p4be5vggcuxeuavbjte
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