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Combinatorial integral approximation

2011
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Mathematical Methods of Operations Research
*

In this study we focus on

doi:10.1007/s00186-011-0355-4
fatcat:wfurxew4zfgivn4es36y7ywlve
*combinatorial*constraints, in particular on restrictions on the number of switches on a fixed time grid. ... In Section 3 we will discuss our new method that is based on a*combinatorial**approximation*of the*integral*over control deviations. ...*Approximating*the*integral*over the controls by MILP techniques The results of Section 2 have been used in several ways. ...##
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Relaxed multibang regularization for the combinatorial integral approximation
[article]

2021
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arXiv
*
pre-print

Multibang regularization and

arXiv:2011.00205v2
fatcat:zsekio6dkrfcbh4fqsljttec7a
*combinatorial**integral**approximation*decompositions are two actively researched techniques for integer optimal control. ... We extend the algorithmic framework of the*combinatorial**integral**approximation*such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control ...*integral**approximation*. ...##
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Combinatorial Integral Approximation Decompositions for Mixed-Integer Optimal Control

2022
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Algorithms
*

Here, a priori bounds were derived for a decomposition into one continuous nonlinear control problem and one mixed-integer linear program, the

doi:10.3390/a15040121
fatcat:udjkf7rbtjbyhoer3bxws2snmi
*combinatorial**integral**approximation*(CIA) problem. ... These extensions are transferable in a straightforward way, though, to recently suggested variants for certain partial differential equations, for algebraic equations, for additional*combinatorial*constraints ... Scaled*Combinatorial**Integral**Approximation*Our hypothesis is that the MILPs based on a scaled*combinatorial**integral**approximation*perform the best on instances where the binary control enters the control ...##
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The Lagrangian relaxation for the combinatorial integral approximation problem

2014
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Optimization Methods and Software
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We decompose this MINLP into an NLP and an MILP, which is called the

doi:10.1080/10556788.2014.890196
fatcat:ghtafktsiraptp7gzw2x7qh62a
*combinatorial**integral**approximation*problem (CIAP). ... We are interested in methods to solve mixed-integer nonlinear optimal control problems (MIOCPs) constrained by ordinary differential equations and*combinatorial*constraints on some of the control functions ... The*combinatorial**integral**approximation*problem (CIAP) arises as a consequence of the following theorem from (15) . Theorem 1 (*Integral**Approximation*Theorem). ...##
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Compactness and convergence rates in the combinatorial integral approximation decomposition

2020
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Mathematical programming
*

AbstractThe

doi:10.1007/s10107-020-01598-8
fatcat:3by2lyyup5d7nc4zmebiqjxtbm
*combinatorial**integral**approximation*decomposition splits the optimization of a discrete-valued control into two steps: solving a continuous relaxation of the discrete control problem, and ... computing a discrete-valued*approximation*of the relaxed control. ... We use the results on convexification reformulations and the*combinatorial**integral**approximation*(CIA) decomposition from [12, 15, 21, 23, 24, 26, 27, 36] . ...##
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On structural similarities of combinatorial integral approximation and binary trust-region steepest descent
[article]

2022
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arXiv
*
pre-print

*Combinatorial*

*integral*

*approximation*and binary trust-region steepest descent are two approaches for the solution of optimal control problems with discrete (binary in the latter case) control inputs. ... The main difference in their analyses is an additional compactness assumption on the reduced objective functional for the

*combinatorial*

*integral*decomposition that implies an

*approximation*of stationary ...

*Combinatorial*

*integral*

*approximation*[8, 12, 23, 22] The idea that underlies CIA is to split the solution process of (P) into solving the continuous relaxation (R) and then computing a V -valued

*approximation*...

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Sherali-Adams Integrality Gaps Matching the Log-Density Threshold

2018
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International Workshop on Approximation Algorithms for Combinatorial Optimization
*

These

doi:10.4230/lipics.approx-random.2018.10
dblp:conf/approx/ChlamtacM18
fatcat:3l7ydhovxraqfaeka7fxtkdcsy
*approximations*have been conjectured to be optimal based on various instantiations of a general conjecture: that it is hard to distinguish a fully random*combinatorial*structure from one which contains ... This gives strong*integrality*gaps which exactly match the gap in the above distinguishing problems, as well as the best-known*approximations*, for Densest k-Subgraph, Smallest p-Edge Subgraph, their hypergraph ... For this problem we get*integrality*gaps matching the*approximation*guarantee of [13] : (1) . Corollary 5. ...##
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On the Integrality Gap of the Prize-Collecting Steiner Forest LP

2017
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International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Our results thus show a separation between the

doi:10.4230/lipics.approx-random.2017.17
dblp:conf/approx/KonemannOP0SV17
fatcat:kis2fag6fndpfchfyslh7gkqau
*integrality*gaps of the LP-relaxations for prize-collecting and non-prize-collecting (i.e., standard) Steiner forest, as well as the*approximation*ratios ... We dispel this belief by showing that the*integrality*gap of this LP is at least 9/4. This holds even for planar graphs. ... This research was initiated during the Hausdorff Trimester Program "*Combinatorial*Optimization". ...##
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Dual Growth with Variable Rates: An Improved Integrality Gap for Steiner Tree
[article]

2022
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arXiv
*
pre-print

In this paper, we extend the approach provided by these authors and show that the

arXiv:1704.08680v6
fatcat:55x76hwamndj3ej64o6s3hvzem
*integrality*gap of BCR is at most 7/6 on quasi-bipartite graphs via a fast*combinatorial*algorithm. ... Using this, they gave a √(2)-*approximation*algorithm for quasi-bipartite graphs and showed that the*integrality*gap of the relaxation is at most 4/3 for this class of graphs. ...*combinatorial*optimization problems. ...##
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A Combinatorial Optimized Knapsack Linear Space for Information Retrieval

2021
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Computers Materials & Continua
*

In this work, we consider the strength of a term and the influence of a term as a

doi:10.32604/cmc.2021.012796
fatcat:zunc3g6a6fbg5by4qodciifuiq
*combinatorial*optimization, called*Combinatorial*Optimized Linear Space Knapsack for Information Retrieval (COLSK-IR). ... However, the influence of the terms that coexist with each other can be part of the frequency of the terms of their semantic dependence, as they are non-*integrative*and their individual meaning cannot ... Moreover, the*approximation*factor with perturbation sets in the COLSK-IR method considers both the non-*integrative*and*integrative*snippets to reduce the convergent time on semantic data analysis by 45% ...##
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Preface

2015
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Mathematical programming
*

In the past years,

doi:10.1007/s10107-015-0869-2
fatcat:epqoua7uqbcupmakq7kurfegbm
*combinatorial*optimization has undergone rapid developments, major advances being obtained in different areas such as computational complexity,*approximation*algorithms, cutting-plane ... edition of ISCO was the second of a series of biennial conferences on*combinatorial*optimization with its first venue held in Hammamet, Tunisia in March 2010. ... They give a 3/2-*approximation*algorithm for this class improving a 2-*approximation*algorithm given before by Goemans and Williamson. ...##
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Computational identities for extensions of some families of special numbers and polynomials

2021
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Turkish Journal of Mathematics
*

Furthermore, we provide an

doi:10.3906/mat-2101-83
fatcat:y7olaz2kw5es5fzvnzp44s6pxq
*approximation*for the*combinatorial*-type 11 numbers with the aid of the Stirling's*approximation*for factorials. ... By the implementation of the p -adic*integral*approach 9 to the*combinatorial*-type polynomials with multi-variables, we also obtain formulas for the Volkenborn*integral*and the 10 fermionic p -adic*integral*... the p -adic*integrals*approach to the*combinatorial*-type polynomials with 12 the Volkenborn and fermionic p -adic*integrals*, we obtain some formulas for the Volkenborn and fermionic p-13 adic*integrals*...##
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Page 14 of Annals of Mathematics Vol. 38, Issue 1
[page]

1937
*
Annals of Mathematics
*

The

*combinatory*invariants of complexes are properties in the large, and as such they have been extended to sets by means of*approximation*. ... The possibility of applying*combinatory*methods in general topology is based entirely on*approximation*of sets by complexes and cycles, and this also explains the character of the results, which express ...##
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On the relationship between algebra and analysis

1980
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Journal of Pure and Applied Algebra
*

The functions and the

doi:10.1016/0022-4049(80)90092-4
fatcat:ruatrtpr4feodj5t2dflt2f3qq
*integral*operator are interpreted*combinatorially*. i=O linearly interpolated, provide a piecewise linear*approximation*to the solution, y. ... Note that y(x) is also an exact fixed point for the*combinatorial**integral*operator T. us model the method of successive*approximations*in the system C(21'tk) (O~jsm). ...##
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Front Matter, Table of Contents, Preface, Program Committees, External Reviewers, List of Authors

2016
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International Workshop on Approximation Algorithms for Combinatorial Optimization
*

Cohen, Cameron Musco, and Jakub Pachocki . . . . . . . . . . . . . . . . . . . . . . . . 7:1-7:18 Oblivious Rounding and the

doi:10.4230/lipics.approx-random.2016.0
dblp:conf/approx/X16
fatcat:5aka2x4msbawlcwc55jleb3htm
*Integrality*Gap Uriel Feige, Michal Feldman, and Inbal Talgam-Cohen . . . . ... into Constant-Dimensional p Spaces Artūrs Bačkurs and Anastasios Sidiropoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1:1-1:15 Computing*Approximate*PSD Factorizations ... Preface This volume contains the papers presented at the 19th International Workshop on*Approximation*Algorithms for*Combinatorial*Optimization Problems (APPROX 2016) and the 20th International Workshop ...
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