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The linearization problem of a binary quadratic problem and its applications [article]

Hao Hu, Renata Sotirov
2020 arXiv   pre-print
Our algorithm gives a complete characterization of the set of linearizable matrices for the quadratic shortest path problem.  ...  Finally, we present a polynomial-time algorithm for the linearization problem of the quadratic shortest path problem on directed acyclic graphs.  ...  Binary quadratic problems In this section, we introduce binary quadratic problems and their two special cases; the quadratic assignment problem and the quadratic shortest path problem.  ... 
arXiv:1802.02426v3 fatcat:wq2iw5bsevgsrmm4qrsrqlrdcy

Special cases of the quadratic shortest path problem

Hao Hu, Renata Sotirov
2017 Journal of combinatorial optimization  
instance of the shortest path problem.  ...  The quadratic shortest path problem (QSPP) is the problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction  ...  Acknowledgements The authors would like to thank two anonymous referees for suggestions that led to an improvement of this paper.  ... 
doi:10.1007/s10878-017-0219-9 fatcat:y7zgj7xysja4lmope2emdlnnt4

Special cases of the quadratic shortest path problem [article]

Hao Hu, Renata Sotirov
2017 arXiv   pre-print
instance of the shortest path problem.  ...  The quadratic shortest path problem (QSPP) is blackthe problem of finding a path with prespecified start vertex s and end vertex t in a digraph such that the sum of weights of arcs and the sum of interaction  ...  Acknowledgements The authors would like to thank two anonymous referees for suggestions that led to an improvement of this paper.  ... 
arXiv:1611.07682v2 fatcat:55p4of6i45f6vkvuzoixybv4pm

Combinatorial Optimization Problems with Interaction Costs: Complexity and Solvable Cases [article]

Stefan Lendl, Ante Ćustić, Abraham P. Punnen
2017 arXiv   pre-print
We show how various topics from different areas in the literature can be formulated as special cases of COPIC.  ...  and special structures of the interaction costs.  ...  Most quadratic combinatorial optimization problems can also be viewed as special cases of COPIC, including the quadratic minimum spanning tree problem [4] , quadratic set covering problem [5] , quadratic  ... 
arXiv:1707.02428v1 fatcat:n7uilbc2ezhapoousweapfu65q

The Quadratic Cycle Cover Problem: special cases and efficient bounds [article]

Frank de Meijer, Renata Sotirov
2019 arXiv   pre-print
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized.  ...  In this paper we study the linearization problem for the quadratic cycle cover problem and related lower bounds.  ...  Acknowledgements We would like to thank two anonymous reviewers for their insightful comments and suggestions to improve an earlier version of this work.  ... 
arXiv:1904.02914v2 fatcat:eozo2ij36bazjkd732xekv4bgu

The quadratic cycle cover problem: special cases and efficient bounds

Frank de Meijer, Renata Sotirov
2020 Journal of combinatorial optimization  
The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized.  ...  In this paper we study the linearization problem for the quadratic cycle cover problem and related lower bounds.  ...  Acknowledgements We would like to thank two anonymous reviewers for their insightful comments and suggestions to improve an earlier version of this work.  ... 
doi:10.1007/s10878-020-00547-7 fatcat:cwlzy6tz3va3zhtifomko53riq

On Solving the Quadratic Shortest Path Problem [article]

Hao Hu, Renata Sotirov
2017 arXiv   pre-print
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized.  ...  We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order m+1, where m is the number of arcs in the graph.  ...  The authors would like to thank Henry Wolkowicz and Lieven Vandenberghe for useful discussions on the ADMM and facial reduction.  ... 
arXiv:1708.06580v1 fatcat:mwwr6safura7vavbmxi4bdpuzi

Trajectory generation for a class of nonlinear systems with input and state constraints

S.K. Kim, D.M. Tilbury
2001 Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148)  
Traditionally the planning stage has either been done from a purely geometrical point of view without regarding the dynamic constraints of the system, or by time-consuming numerical optimization including  ...  This paper presents a new way to generate a trajectory quickly when a nonlinear system is input-output linearizable while satisfying the dynamic constraints.  ...  We consider the special case of this problem when the nonlinear system is input-output linearizable.  ... 
doi:10.1109/acc.2001.945762 fatcat:zr2h7wbtgne27dsvq26l2ndwhm

Polynomial-Time Data Reduction for Weighted Problems Beyond Additive Goal Functions [article]

Matthias Bentert and René van Bevern and Till Fluschnik and André Nichterlein and Rolf Niedermeier
2021 arXiv   pre-print
Sci. 2017] used a technique of Frank and Tardos [Combinatorica 1987] to obtain polynomial-size kernels for weighted problems, mostly with additive goal functions.  ...  with size upper-bounded by a function of a parameter chosen in advance.  ...  Tsidulko from Novosibirsk State University for pointing out how to apply the Frank-Tardos theorem to the Uncapacitated Facility Location problem (Section 5.1).  ... 
arXiv:1910.00277v4 fatcat:rv46nhigtfalbo7dmv7f7dpdge

Linearization: Geometric, Complex, and Conditional

Asghar Qadir
2012 Journal of Applied Mathematics  
Of special interest is the procedure that Lie developed to transform scalar nonlinear second-order ordinary differential equations to linear form.  ...  It is relevant to mention that much of the work isnotlinearization but uses the base of linearization.  ...  He is also grateful to DECMA and the School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, South Africa, for support at the Galois Bicentenary Conference SDEA-I  ... 
doi:10.1155/2012/303960 fatcat:xi7ua5iwezf6jpuuu7b4q47ag4

A class of exponential neighbourhoods for the quadratic travelling salesman problem [article]

Brad Woods, Abraham Punnen
2019 arXiv   pre-print
We also show that the quadratic shortest path problem on an acyclic digraph can be solved in pseudopolynomial time and by an FPTAS when the rank of the associated cost matrix is fixed.  ...  It is shown that fixed-rank QTSP is solvable in pseudopolynomial time and admits an FPTAS for each of the special cases studied, except for the case of matching edge ejection tours.  ...  Noting that the exact shortest path problem is NP-hard, we relax the problem to the problem of finding a shortest walk that minimizes the QSPP(p,H) objective function.  ... 
arXiv:1705.05393v2 fatcat:csa67kte2reh7duvfjuc2x5y2m

Nonlinear Stabilization via Control Contraction Metrics: a Pseudospectral Approach for Computing Geodesics [article]

Karen Leung, Ian R. Manchester
2017 arXiv   pre-print
We compare the performance of a CCM controller with other popular feedback control techniques, namely the Linear Quadratic Regulator (LQR) and Nonlinear Model Predictive Control (NMPC).  ...  Through a case study of a stiff nonlinear system, we highlight two key benefits: (i) using CCM for nonlinear stabilization and (ii) rapid online computations amenable to real-time implementation.  ...  Direct methods involve discretizing a shortest path or optimal control problem, and then solving the resulting nonlinear problem (NLP) using generic methods and this is the approach taken in this paper  ... 
arXiv:1607.04340v2 fatcat:ow7cot7jjvfk7gn5ngqrappmee

Synthesizing concurrent schedulers for irregular algorithms

Donald Nguyen, Keshav Pingali
2011 Proceedings of the sixteenth international conference on Architectural support for programming languages and operating systems - ASPLOS '11  
parallel programming problem further.  ...  Moreover, the amount of work can vary dramatically with the scheduling policy.  ...  We are also grateful to Milind Kulkarni (Purdue) and Roman Manevich (UT Austin) for their suggestions for improving the paper.  ... 
doi:10.1145/1950365.1950404 dblp:conf/asplos/NguyenP11 fatcat:cvcue47xjzakvmv4ydxnyre44i

Synthesizing concurrent schedulers for irregular algorithms

Donald Nguyen, Keshav Pingali
2011 SIGPLAN notices  
parallel programming problem further.  ...  Moreover, the amount of work can vary dramatically with the scheduling policy.  ...  We are also grateful to Milind Kulkarni (Purdue) and Roman Manevich (UT Austin) for their suggestions for improving the paper.  ... 
doi:10.1145/1961296.1950404 fatcat:evlcssc7ejbgppeutu7iz2l2i4

Synthesizing concurrent schedulers for irregular algorithms

Donald Nguyen, Keshav Pingali
2011 SIGARCH Computer Architecture News  
parallel programming problem further.  ...  Moreover, the amount of work can vary dramatically with the scheduling policy.  ...  We are also grateful to Milind Kulkarni (Purdue) and Roman Manevich (UT Austin) for their suggestions for improving the paper.  ... 
doi:10.1145/1961295.1950404 fatcat:pp7egwsxurd7pivmdmvqdxcb6a
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