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Atomic Set Constraints with Projection
[chapter]

2002
*
Lecture Notes in Computer Science
*

We investigate a class of

doi:10.1007/3-540-45610-4_22
fatcat:snstgyv7bvgtbjjc3pvqnnfdv4
*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*. ...##
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Ray projection for optimizing polytopes with prohibitively many constraints in set-covering column generation

2014
*
Mathematical programming
*

A recurrent task in mathematical programming consists of optimizing polytopes

doi:10.1007/s10107-014-0840-7
fatcat:3i3x75hlunhgnkvuslvdken644
*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*. ...##
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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

2017
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Operations Research and Fuzziology
*

求解带有稀疏约束和闭凸集约束的优化问题的投影算法

In this paper, we mainly consider the optimization problem

doi:10.12677/orf.2017.73009
fatcat:ddj2ck6xgbhwddrlbblhx3wwci
*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. ...##
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A generalized gradient projection method based on a new working set for minimax optimization problems with inequality constraints

2017
*
Journal of Inequalities and Applications
*

Combining the techniques of the working

doi:10.1186/s13660-017-1321-3
pmid:28298875
pmcid:PMC5329097
fatcat:7vtopqddlbdrxby5anlydiru54
*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*. ...##
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Optimization of intensity modulated beams with volume constraints using two methods: Cost function minimization and projections onto convex sets

1998
*
Medical Physics (Lancaster)
*

The second technique is based on the theory of

doi:10.1118/1.598218
pmid:9571609
fatcat:ozx3bqzor5aqjk52rfv2h7qvs4
*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*. ...##
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Set constraints with projections are in NEXPTIME

*
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

doi:10.1109/sfcs.1994.365727
dblp:conf/focs/CharatonikP94
fatcat:pjqh566jsbfgpo2yim3ucleyiq
*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*...##
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Kernel synthesis for generalized time-frequency distributions using the method of alternating projections onto convex sets

1994
*
IEEE Transactions on Signal Processing
*

If there exists a nonempty intersection among the

doi:10.1109/78.298273
fatcat:vlx7hhenb5fsllhullmxmqtpty
*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. ...##
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Kernel synthesis for generalized time-frequency distributions using the method of projections onto convex sets

1990
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Advanced Signal Processing Algorithms, Architectures, and Implementations
*

Thus, for a given

doi:10.1117/12.23477
fatcat:54dah3be5vdrzgcmwionqpwdqq
*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. ...##
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Projection merging

2000
*
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '00
*

Combined

doi:10.1145/325694.325706
dblp:conf/popl/SuFA00
fatcat:xqqec2q34ndyxgja4jzeemmeda
*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] . ...##
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An evaluation of project completion with application of fuzzy set theory

2012
*
Management
*

The paper aims Vol.16, No. 1 An evaluation of

doi:10.2478/v10286-012-0016-6
fatcat:cki2qeil3zc3jfejcfi53smusa
*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 ...##
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Algorithms and software for projections onto intersections of convex and non-convex sets with applications to inverse problems
[article]

2019
*
arXiv
*
pre-print

We propose algorithms and software for computing

arXiv:1902.09699v2
fatcat:yp3t7tfj6jaulcgtvxe5ejqlkm
*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 ...##
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Face Recognition with the Multiple Constrained Mutual Subspace Method
[chapter]

2005
*
Lecture Notes in Computer Science
*

To extract effective features for identification both subspaces are

doi:10.1007/11527923_8
fatcat:7ctzfgzv4jeglcpqw7n3ntgfgi
*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. ...##
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Fast Gradient Method for Model Predictive Control with Input Rate and Amplitude Constraints

2020
*
IFAC-PapersOnLine
*

This paper is concerned

doi:10.1016/j.ifacol.2020.12.070
fatcat:s3wbh34gezhjdcymlxs3k6ilb4
*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. ...##
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A unified approach for inversion problems in intensity-modulated radiation therapy

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

doi:10.1088/0031-9155/51/10/001
pmid:16675857
fatcat:d3r6o54knzgfbhwpk2ik2fnxqu
*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) = ...##
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An implementation of CAD in Maple utilising problem formulation, equational constraints and truth-table invariance
[article]

2013
*
arXiv
*
pre-print

Cylindrical algebraic decomposition (CAD) is an important tool for the investigation of semi-algebraic

arXiv:1306.3062v1
fatcat:elchxozizvbhph6qhxyg3aznqi
*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*...
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