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Atomic Set Constraints with Projection [chapter]

Witold Charatonik, Jean-Marc Talbot
2002 Lecture Notes in Computer Science  
We investigate a class of set constraints defined as atomic set constraints augmented with projection.  ...  This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints.  ...  This is no longer the case for atomic set constraints with projection.  ... 
doi:10.1007/3-540-45610-4_22 fatcat:snstgyv7bvgtbjjc3pvqnnfdv4

Ray projection for optimizing polytopes with prohibitively many constraints in set-covering column generation

Daniel Porumbel
2014 Mathematical programming  
A recurrent task in mathematical programming consists of optimizing polytopes with prohibitivelymany constraints, e.g., the primal polytope in cutting-planes methods or the dual polytope in Column Generation  ...  This is confirmed by numerical experiments on various capacitated Set-Covering problems: Capacitated Arc-Routing, Cutting-Stock and other three versions of Elastic Cutting-Stock (i.e., a problem class  ...  Conclusions We proposed a ray projection approach for optimizing (primal or dual) LPs in which the feasible area is a polytope P with prohibitively many constraints.  ... 
doi:10.1007/s10107-014-0840-7 fatcat:3i3x75hlunhgnkvuslvdken644

A Projection Algorithm for Solving Optimization Problems with Sparsity Constraints and Closed Convex Set Constraints
求解带有稀疏约束和闭凸集约束的优化问题的投影算法

军 孙
2017 Operations Research and Fuzziology  
In this paper, we mainly consider the optimization problem with sparsity constraints and closed convex set constraints.  ...  We design a gradient projection algorithm with Armijo step size rule, and prove that the sequence of the iteration generated by this algorithm can converge to an α-stationary point of the problem.  ... 
doi:10.12677/orf.2017.73009 fatcat:ddj2ck6xgbhwddrlbblhx3wwci

A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

Guodong Ma, Yufeng Zhang, Meixing Liu
2017 Journal of Inequalities and Applications  
Combining the techniques of the working set identification and generalized gradient projection, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality  ...  constraints.  ...  In this paper, we present a new generalized gradient projection algorithm for minimax optimization problems with inequality constraints.  ... 
doi:10.1186/s13660-017-1321-3 pmid:28298875 pmcid:PMC5329097 fatcat:7vtopqddlbdrxby5anlydiru54

Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets

Paul S. Cho, Shinhak Lee, Robert J. Marks, Seho Oh, Steve G. Sutlief, Mark H. Phillips
1998 Medical Physics (Lancaster)  
The second technique is based on the theory of projections onto convex sets ͑POCS͒ in which the dose-volume constraint is replaced by a limit on integral dose.  ...  The convex projection method can find solutions in much shorter time with minimal user interaction. © 1998 American Association of Physicists in Medicine. ͓S0094-2405͑98͒01004-9͔  ...  Dose-volume histograms for the rectum obtained with ͑a͒ the cost function minimization method and with ͑b͒ the method of projections onto convex sets.  ... 
doi:10.1118/1.598218 pmid:9571609 fatcat:ozx3bqzor5aqjk52rfv2h7qvs4

Set constraints with projections are in NEXPTIME

W. Charatonik, L. Pacholski
Proceedings 35th Annual Symposium on Foundations of Computer Science  
In this paper we prove that the problem of existence of a solution of a system of set constraints with projections is in NEXPTIME, and thus that it is NEXPTIMEcomplete. This extends the result of A .  ...  Systems of set constraints describe relations between sets of ground terms. They have been successfully used in program analysis and type inference.  ...  It was noticed in [7] that negated inclusion can be expressed by positive set constraints in the presence of projections, thus the class of set constraints (with projections) contains the class of set  ... 
doi:10.1109/sfcs.1994.365727 dblp:conf/focs/CharatonikP94 fatcat:pjqh566jsbfgpo2yim3ucleyiq

Kernel synthesis for generalized time-frequency distributions using the method of alternating projections onto convex sets

S. Oh, R.J. Marks, L.E. Atlas
1994 IEEE Transactions on Signal Processing  
If there exists a nonempty intersection among the constraint sets, then the theory of alternating projection onto convex sets (POCS) guarantees convergence to a kernel that satisfies all of the constraints  ...  If the constraints can be partitioned into two sets, each with a nonempty intersection, then POCS guarantees convergence to a kernel that satisfies the inconsistent constraints with minimum mean-square  ...  In other words, if a function is already within the set, then the projection is This constraint can prohibit the projection onto convex sets an identity operation.  ... 
doi:10.1109/78.298273 fatcat:vlx7hhenb5fsllhullmxmqtpty

Kernel synthesis for generalized time-frequency distributions using the method of projections onto convex sets

Seho Oh, Robert J. Marks II, Les E. Atlas, James W. Pitton, Franklin T. Luk
1990 Advanced Signal Processing Algorithms, Architectures, and Implementations  
Thus, for a given set of constraints, the kernel can be designed by alternately projecting among these sets.  ...  If the constraints can be partitioned into two sets, each with a nonempty intersection, then POCS guarantees convergence to a kernel that satisfies the inconsistent constraints with minimum mean square  ...  We illustrate with sample projection operators from the convex constraints of the Cohen kernel in the previous section.  ... 
doi:10.1117/12.23477 fatcat:54dah3be5vdrzgcmwionqpwdqq

Projection merging

Zhendong Su, Manuel Fähndrich, Alexander Aiken
2000 Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '00  
Combined with cycle elimination 7], projection merging achieves orders of magnitude speedup of analysis time on programs over that of using cycle elimination alone.  ...  We present projection merging, a technique to reduce path redundancy.  ...  Set Constraints This subsection covers basic material on set constraints. In particular, we work with a subset of the full language of set constraints 2, 12] .  ... 
doi:10.1145/325694.325706 dblp:conf/popl/SuFA00 fatcat:xqqec2q34ndyxgja4jzeemmeda

An evaluation of project completion with application of fuzzy set theory

Marcin Relich
2012 Management  
The paper aims Vol.16, No. 1 An evaluation of project completion with application of fuzzy set theory to present a problem of project management in terms of fuzzy constraints satisfaction problem, and  ...  Vol. 16, No. 1 An evaluation of project completion with application of fuzzy set theory The implementation of considered approach in form of constraint programming languages imposes some assumptions  ... 
doi:10.2478/v10286-012-0016-6 fatcat:cki2qeil3zc3jfejcfi53smusa

Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems [article]

Bas Peters, Felix J. Herrmann
2019 arXiv   pre-print
We propose algorithms and software for computing projections onto the intersection of multiple convex and non-convex constraint sets.  ...  Our algorithms outperform the well known Dykstra's algorithm when individual sets are not easy to project onto because we exploit similarities between constraint sets.  ...  PARSDMM computes matrix-vector producs with the sparsity pattern of A A (this pattern overlaps with the the linear operators in the other two sets). • projections onto the box constraint set and the 1  ... 
arXiv:1902.09699v2 fatcat:yp3t7tfj6jaulcgtvxe5ejqlkm

Face Recognition with the Multiple Constrained Mutual Subspace Method [chapter]

Masashi Nishiyama, Osamu Yamaguchi, Kazuhiro Fukui
2005 Lecture Notes in Computer Science  
To extract effective features for identification both subspaces are projected onto multiple constraint subspaces. For generating constraint subspaces we apply ensemble learning algorithms, i.e.  ...  In our method we represent the set of patterns as a low-dimensional subspace, and calculate the similarity between an input subspace and a reference subspace, representing learnt identity.  ...  (e)Multiple CMSM with Bagging (MCMSM-Bagging) The similarity was determined with MSM after projecting onto multiple constraint subspaces.  ... 
doi:10.1007/11527923_8 fatcat:7ctzfgzv4jeglcpqw7n3ntgfgi

Fast Gradient Method for Model Predictive Control with Input Rate and Amplitude Constraints

Idris Kempf, Paul Goulart, Stephen Duncan
2020 IFAC-PapersOnLine  
This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs.  ...  Abstract: This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs.  ...  set U as defined in (7) with r = a = 1.  ... 
doi:10.1016/j.ifacol.2020.12.070 fatcat:s3wbh34gezhjdcymlxs3k6ilb4

A unified approach for inversion problems in intensity-modulated radiation therapy

Yair Censor, Thomas Bortfeld, Benjamin Martin, Alexei Trofimov
2006 Physics in Medicine and Biology  
The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraints sets.  ...  ., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints.  ...  The general iterative gradient projection scheme, with the stepsize s, designed to find a minimum of F (x) subject to x ∈ Ω, where Ω ⊆ R J is some constraint set, whose projector is P Ω , is: x (k+1) =  ... 
doi:10.1088/0031-9155/51/10/001 pmid:16675857 fatcat:d3r6o54knzgfbhwpk2ik2fnxqu

An implementation of CAD in Maple utilising problem formulation, equational constraints and truth-table invariance [article]

Matthew England
2013 arXiv   pre-print
Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic sets, with applications within algebraic geometry and beyond.  ...  We describe how the CADs produced using equational constraints are able to take advantage of not just improved projection but also improvements in the lifting phase.  ...  Extra polynomials have been added to the projection set sufficient to allow the conclusion that: (a) the CAD is sign-invariant with respect to all the equational constraints and all the other constraints  ... 
arXiv:1306.3062v1 fatcat:elchxozizvbhph6qhxyg3aznqi
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