citations.bib

@BOOK{Cox-Little-Shea97,
  Author =		 {Cox,David and Little, John and O'Shea, Donald},
  Title =	  	 {Ideals, Varieties, and Algorithms : An Introduction
                  to Computational Algebraic Geometry and Commutative
                  Algebra},
  Publisher =	 {Springer},
  Address =		 {New York, U{SA}},
  Series =		 {Undergraduate Texts in Mathematics},
  Signature =	 {2005-382},
  Year =		   {1997},
  Pages =		   {536},
  Edition =		 {2nd},
  ISSN_ISBN =	 {0-387-94680-2},
  hardcopy =	 {CMP.book.A347},
  pincode =		 {3102005347},
}

@book{Nesterov-2004,
  author =     {Nesterov,Yurii},
  title =      {Introductory lectures on convex optimization : A basic course},
  publisher =  {Springer},
  year =       {2004},
  pages =      {236},
  ISBN =       {1402075537},
  signature =  {2014-26, 13133},
  hardcopy =   {CMP.book.A550 },
}

@incollection{Karp1972,
  author =     {Karp, Richard M.},
  title =      {Reducibility among Combinatorial Problems},
  bookTitle =  {Complexity of Computer Computations},
  year =       {1972},
  publisher =  {Springer US},
  address =    {Boston, MA},
  pages =      {85--103},
  isbn =       {978-1-4684-2001-2},
  doi =        {10.1007/978-1-4684-2001-2_9},
  url =        {http://dx.doi.org/10.1007/978-1-4684-2001-2_9}
}

@article{MAX-CUT,
  author =     {Goemans, Michel X. and Williamson, David P.},
  title =      {Improved Approximation Algorithms for Maximum Cut and Satisfiability Problems Using Semidefinite Programming},
  journal =    {Journal of the ACM},
  issue_date = {November 1995},
  volume =     {42},
  number =     {6},
  month =      {November},
  year =       {1995},
  issn =       {0004-5411},
  pages =      {1115--1145},
  numpages =   {31},
  url =        {http://doi.acm.org/10.1145/227683.227684},
  doi =        {10.1145/227683.227684},
  acmid =      {227684},
  publisher =  {ACM},
  address =    {New York, NY, USA},
  keywords =   {Approximation algorithms, convex optimization, randomized algorithms, satisfiability},
} 

@Book{Becker93,
  author =     {Becker, Thomas and Weispfenning, Volker},
  title =      {Gr{\"o}bner Bases, A Computational Approach to Commutative Algebra},
  publisher =  {Springer-Verlag},
  address =    {New York, NY},
  year =       {1993},
  isbn =       {0-387-97971-9},
  series =     {Graduate Texts in Mathematics},
  number =     {141},
  hardcopy =   {CMP.book.A411},
  signature =  {2006-940},
  pincode =    {3102003215},
}

@article{F4,
  Author =     {Faug\`ere,Jean-Charles},
  Title =      {A new efficient algorithm for computing Gr\"obner bases ($F_4$)},
  Journal =    {Journal of pure and applied algebra},
  Year =       {1999},
  Number =     {1--3},
  Pages =      {61--88},
  Volume =     {139},
  Month =      {July},
  Publisher =  {Elsevier},
  url =        {http://www-salsa.lip6.fr/~jcf/Papers/F99a.pdf},
}

@incollection{SOS,
  author =     {Laurent, Monique},
  title =      {Sums of Squares, Moment Matrices and Optimization Over Polynomials},
  bookTitle =  {Emerging Applications of Algebraic Geometry},
  year =       {2009, Updated version from 2010},
  publisher =  {Springer New York},
  pages =      {157--270},
  note =       {\url{http://homepages.cwi.nl/~monique/files/moment-ima-update-new.pdf} [Online; accessed 2017-05-05]},
  isbn =       {978-0-387-09686-5},
  doi =        {10.1007/978-0-387-09686-5_7},
  url =        {http://dx.doi.org/10.1007/978-0-387-09686-5_7}
}

@article{Lasserre,
  author =     {Lasserre, Jean B.},
  title =      {Global Optimization with Polynomials and the Problem of Moments},
  journal =    {Society for Industrial and Applied Mathematics Journal on Optimization},
  year =       {2001},
  volume =     {11},
  pages =      {796--817}
}

@misc{HenrionLectures,
  author =     {Henrion, Didier},
  title =      {Optimization on linear matrix inequalities for polynomial systems control},
  month =      {September},
  year =       {2014}
}

@article{gloptipoly,
  author =     {Henrion, Didier and Lasserre, Jean-Bernard and L\"ofberg, Johan},
  title =      {GloptiPoly 3: Moments, Optimization and Semidefinite Programming},
  journal =    {Optimization Methods Software},
  issue_date = {August 2009},
  volume =     {24},
  number =     {4--5},
  month =      {August},
  year =       {2009},
  pages =      {761--779},
  numpages =   {19},
  url =        {http://dx.doi.org/10.1080/10556780802699201},
  publisher =  {Taylor \& Francis, Inc.},
  address =    {Bristol, PA, USA},
  keywords =   {global optimization, moments, polynomials, semidefinite programming},
}

@inproceedings{AutoGen,
  author =     {Kukelova,Zuzana and Bujnak,Martin and Pajdla,Tomas},
  title =      {Automatic Generator of Minimal Problem Solvers},
  year =       {2008},
  series =     {ECCV 2008},
  location =   {Marseille, France},
  month =      {October 12--18},
  booktitle =  {Proceedings of The 10th European Conference on Computer Vision},
}

@article{MomentMethodReal,
  author =     {Lasserre, Jean Bernard and Laurent, Monique and Rostalski, Philipp},
  title =      {Semidefinite Characterization and Computation of Zero-Dimensional Real Radical Ideals},
  journal =    {Foundations of Computational Mathematics},
  issue_date = {October 2008},
  volume =     {8},
  number =     {5},
  month =      {October},
  year =       {2008},
  issn =       {1615-3375},
  pages =      {607--647},
  numpages =   {41},
  url =        {https://doi.org/10.1007/s10208-007-9004-y},
  publisher =  {Springer-Verlag New York, Inc.},
  address =    {Secaucus, NJ, USA},
  keywords =   {(Real) radical ideal, 12D10, 12E12, 13P10, 14P05, 90C22, Algebraic geometry, Semidefinite programming, Zero-dimensional ideal},
}

@inproceedings{MomentMethodComplex,
  author =     {Lasserre, Jean Bernard and Laurent, Monique and Rostalski, Philipp},
  title =      {A Unified Approach to Computing Real and Complex Zeros of Zero-Dimensional Ideals},
  booktitle =  {Emerging Applications of Algebraic Geometry},
  year =       {2009},
  publisher =  {Springer New York},
  address =    {New York},
  pages =      {125--155},
  url =        {https://doi.org/10.1007/978-0-387-09686-5_6}
}

@inproceedings{MomentMethod,
  author =     {Laurent, Monique and Rostalski, Philipp},
  title =      {The Approach of Moments for Polynomial Equations},
  booktitle =  {Handbook on Semidefinite, Conic and Polynomial Optimization},
  year =       {2012},
  publisher =  {Springer US},
  address =    {Boston, MA},
  pages =      {25--60},
  url =        {https://doi.org/10.1007/978-1-4614-0769-0_2}
}

@inproceedings{Bellman-Fan,
  author =     {Bellman, Richard and Fan, Ky},
  title =      {On Systems of Linear Inequalities in Hermitian Matrix Variables},
  booktitle =  {Convexity: Proceedings of Symposia in Pure Mathematics},
  year =       {1963},
  pages =      {1--11},
  volume =     {7},
  publisher =  {American Mathematical Society Providence},
}

@incollection{Cullum-Donath-Wolfe,
  author =     {Cullum, Jane
                  and Donath, W. E.
                  and Wolfe, P.},
  title =      {The minimization of certain nondifferentiable sums of eigenvalues of symmetric matrices},
  bookTitle =  {Nondifferentiable Optimization},
  year =       {1975},
  publisher =  {Springer Berlin Heidelberg},
  address =    {Berlin, Heidelberg},
  pages=       {35--55},
  isbn =       {978-3-642-00764-4},
  doi =        {10.1007/BFb0120698},
  url =        {http://dx.doi.org/10.1007/BFb0120698}
}

@article{Overton,
  title =      {On minimizing the maximum eigenvalue of a symmetric matrix},
  author =     {Overton,Michael},
  year =       {1988},
  month =      {April},
  volume =     {9},
  pages =      {256--268},
  journal =    {SIAM Journal on Matrix Analysis and Applications},
  issn =       {0895-4798},
  publisher =  {Society for Industrial and Applied Mathematics Publications},
}

@inbook{Pataki,
  place =      {United States},
  title =      {On the multiplicity of optimal eigenvalues},
  publisher =  {University of Michigan, Ann Arbor, MI (United States)},
  author =     {Pataki, Gabor},
  year =       {1994},
  month =      {December}
}

@Article{Karmarkar1984,
  author =     {Karmarkar, Narendra},
  title =      {A new polynomial-time algorithm for linear programming},
  journal =    {Combinatorica},
  year =       {1984},
  volume =     {4},
  pages =      {373--395},
  issn =       {1439-6912},
  doi =        {10.1007/BF02579150},
  url =        {http://dx.doi.org/10.1007/BF02579150}
}

@techreport{Nesterov-Nemirovski,
  title =      {A general approach to polynomial-time algorithms design for convex Programming},
  author =     {Nesterov,Yurii and Nemirovski,Arkadi},
  year =       {1988},
  institution ={Central Economical and Mathematical Institute, USSR Academy of Sciences},
  address =    {Moscow, USSR},
  type =       {Technical report},
}

@book{Python,
  author =     {van Rossum,Guido and Drake,Fred L.},
  title =      {The Python Language Reference Manual},
  publisher =  {Network Theory Ltd},
  year =       {2011},
  pages =      {150},
  ISBN =       {978-1-906966-14-0},
}

@Article{Sedumi,
  author =     {Sturm,Jos F.},
  title =      {Using {SeDuMi} 1.02, a {MATLAB} toolbox for optimization over symmetric cones},
  journal =    {Optimization Methods and Software},
  year =       {1999},
  volume =     {11--12},
  pages =      {625--653},
  note =       {Version 1.05 available from {\url{http://fewcal.kub.nl/sturm}}}
}

@inproceedings{Yalmip,
  address =    {Taipei, Taiwan},
  author =     {L{\"{o}}fberg, Johan},
  booktitle =  {Proceedings of the CACSD Conference},
  title =      {{YALMIP} : A Toolbox for Modeling and Optimization in {MATLAB}},
  year =       {2004}
}

@manual{mosek,
  author =     {{MOSEK ApS}},
  title =      {The MOSEK optimization toolbox for MATLAB manual. Version 7.1 (Revision 28)},
  year =       {2015},
  note =       {\url{http://docs.mosek.com/7.1/toolbox/index.html} [Online; accessed 2017-04-25]}
}

@BOOK{lapack,
  AUTHOR =       {Anderson, E. and Bai, Z. and Bischof, C. and
                    Blackford, S. and Demmel, J. and Dongarra, J. and
                    Du Croz, J. and Greenbaum, A. and Hammarling, S. and
                    McKenney, A. and Sorensen, D.},
  TITLE =        {{LAPACK} Users' Guide},
  EDITION =      {3rd},
  PUBLISHER =    {Society for Industrial and Applied Mathematics},
  YEAR =         {1999},
  ADDRESS =      {Philadelphia, PA},
  ISBN =         {0-89871-447-8 (paperback)}
}

@ARTICLE{atlas,
  AUTHOR =       {R. Clint Whaley and Antoine Petitet},
  TITLE  =       {Minimizing development and maintenance costs in supporting
                    persistently optimized {BLAS}},
  JOURNAL=       {Software: Practice and Experience},
  volume =       {35},
  number =       {2},
  pages  =       {101--121},
  month  =       {February},
  YEAR   =       {2005},
  NOTE   =       {\url{http://www.cs.utsa.edu/~whaley/papers/spercw04.ps} [Online; accessed 2017-04-18]}
}

@article{blas,
  author =       {Lawson, C. L. and Hanson, R. J. and Kincaid, D. R. and Krogh, F. T.},
  title =        {Basic Linear Algebra Subprograms for Fortran Usage},
  journal =      {ACM Trans. Math. Softw.},
  issue_date =   {Sept. 1979},
  volume =       {5},
  number =       {3},
  month =        {September},
  year =         {1979},
  issn =         {0098-3500},
  pages =        {308--323},
  numpages =     {16},
  url =          {http://doi.acm.org/10.1145/355841.355847},
  doi =          {10.1145/355841.355847},
  acmid =        {355847},
  publisher =    {ACM},
  address =      {New York, NY, USA},
}

@TECHREPORT{SDPA,
  author =       {Makoto Yamashita and Katsuki Fujisawa and Kazuhide Nakata and Maho Nakata and Mituhiro Fukuda and Kazuhiro Kobayashi and Kazushige Goto},
  title =        {A high-performance software package for semidefinite programs: {SDPA7}},
  institution =  {},
  year =         {2010},
  month =        {September},
  institution =  {Department of Mathematical and Computing Science, Tokyo Institute of Technology},
  address =      {Tokyo Japan},
  type =         {Technical report},
}

@misc{scs,
  author =       {Brendan O'Donoghue and Eric Chu and Neal Parikh and Stephen P. Boyd},
  title =        {{SCS}: Splitting Conic Solver, version 1.2.6},
  howpublished = {\url{https://github.com/cvxgrp/scs} [Online; accessed 2017-04-22]},
  month =        {April},
  year =         {2016}
}

@article{ransac,
  author =       {Fischler, Martin A. and Bolles, Robert C.},
  title =        {Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography},
  journal =      {Communications of the ACM},
  volume =       {24},
  number =       {6},
  month =        {June},
  year =         {1981},
  issn =         {0001-0782},
  pages =        {381--395},
  numpages =     {15},
  url =          {http://doi.acm.org/10.1145/358669.358692},
  publisher =    {ACM},
  address =      {New York, NY, USA},
  keywords =     {automated cartography, camera calibration, image matching, location determination, model fitting, scene analysis},
}

@article{Shor,
  author =       {Shor, Naum Z.},
  title =        {Class of global minimum bounds of polynomial functions},
  journal =      {Cybernetics},
  year =         {1987},
  month =        {November},
  volume =       {23},
  number =       {6},
  pages =        {731--734},
  issn =         {1573-8337},
  doi =          {10.1007/BF01070233},
  url =          {https://doi.org/10.1007/BF01070233}
}

@incollection{Nesterov-2000,
  author =       {Nesterov, Yurii},
  title =        {Squared Functional Systems and Optimization Problems},
  bookTitle =    {High Performance Optimization},
  year =         {2000},
  publisher =    {Springer US},
  pages =        {405--440},
  isbn =         {978-1-4757-3216-0},
  doi =          {10.1007/978-1-4757-3216-0_17},
  url =          {https://doi.org/10.1007/978-1-4757-3216-0_17}
}

@article{putinar,
  title =        {Positive polynomials on compact semi-algebraic sets},
  author =       {Putinar, Mihai},
  journal =      {Indiana University Mathematics Journal},
  volume =       {42},
  number =       {3},
  pages =        {969--984},
  year =         {1993},
  publisher =    {JSTOR}
}

@article{GpoSolver,
  author =       {Heller, Jan and Pajdla, Tomas},
  title =        {GpoSolver: A Matlab/C++ Toolbox for Global Polynomial Optimization},
  journal =      {Optimization Methods Software},
  issue_date =   {April 2016},
  volume =       {31},
  number =       {2},
  month =        {March},
  year =         {2016},
  issn =         {1055-6788},
  pages =        {405--434},
  numpages =     {30},
  url =          {http://dx.doi.org/10.1080/10556788.2015.1121489},
  doi =          {10.1080/10556788.2015.1121489},
  acmid =        {2890702},
  publisher =    {Taylor \& Francis, Inc.},
  keywords =     {global polynomial optimization, linear matrixinequalities, polynomial matrix inequalities, semidefinite programming relaxations},
}

@MISC{SOSTOOLS,
  author =       {Stephen Prajna and Antonis Papachristodoulou and Peter Seiler and Pablo A. Parrilo},
  title =        {SOSTOOLS: Sum of squares optimization toolbox for MATLAB},
  year =         {2004}
}

@phdthesis{Buchberger,
  author =       {Buchberger, Bruno},
  title =        {Ein Algorithmus zum Auffinden der Basiselemente des Rest\-klassenringes nach einem nulldimensionalen Polynomideal},
  school =       {Mathema\-tical Institute, University of Innsbruck, Austria},
  year =         {1965},
}

@article{5pt,
  author =       {Stewenius,Henrik and Engels,Christopher and Nister,David},
  title =        {Recent Developments on Direct Relative Orientation},
  Journal =      {ISPRS Journal of Photogrammetry and Remote Sensing},
  Year =         {2006},
  Number =       {4},
  Pages =        {284--294},
  Volume =       {60},
  Month =        {May},
}

@article{p3p1841,
  author =       {Grunert, Johann August},
  title =        {Das pothenotische problem in erweiterter gestalt nebst über seine
  anwendungen in der geodäsie},
  journal =      {Grunerts Archiv für Mathematik und Physik},
  pages =        {238--248},
  year =         {1841},
  volume =       {1}
}

@article{p3p,
  author =       {Xiao-Shan Gao and Xiao-Rong Hou and Jianliang Tang and Hang-Fei Cheng},
  journal =      {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  title =        {Complete solution classification for the perspective-three-point problem},
  year =         {2003},
  volume =       {25},
  number =       {8},
  pages =        {930-943},
  keywords =     {computational geometry;computer vision;polynomials;CASSC;P3P equation system;algebraic approach;complete solution classification;geometric approach;perspective-three-point problem;pose estimation;triangular decomposition;zero decomposition algorithm;Algorithm design and analysis;Automatic control;Calibration;Cameras;Equations;Helium;Layout;Robot vision systems;Robotics and automation;Robustness},
  month =        {August}
}

@InProceedings{p35pfwu,
  author =       {Wu, Changchang},
  title =        {P3.5P: Pose Estimation With Unknown Focal Length},
  booktitle =    {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  month =        {June},
  year =         {2015}
}

@InProceedings{p35pf,
  author =       {Larsson, Viktor and Kukelova, Zuzana and Zheng, Yinqiang},
  title =        {Making Minimal Solvers for Absolute Pose Estimation Compact and Robust},
  booktitle =    {The IEEE International Conference on Computer Vision (ICCV)},
  month =        {October},
  year =         {2017}
} 

@misc{ladio,
  title =        {{LADIO}: Live Action Data Input / Output project},
  howpublished = {\url{https://griwodz.github.io/ladioproject/} [Online; accessed 2017-11-09]},
}

@misc{AliceVision,
  title =        {Alice Vision: Photogrammetric Computer Vision Framework},
  howpublished = {\url{https://alicevision.github.io/} [Online; accessed 2017-11-09]},
}

@Article{sift,
  author =       {Lowe, David G.},
  title =        {Distinctive Image Features from Scale-Invariant Keypoints},
  journal =      {International Journal of Computer Vision},
  year =         {2004},
  month =        {November},
  day =          {01},
  volume =       {60},
  number =       {2},
  pages =        {91--110},
  issn =         {1573-1405},
  doi =          {10.1023/B:VISI.0000029664.99615.94},
  url =          {https://doi.org/10.1023/B:VISI.0000029664.99615.94}
}

@INPROCEEDINGS{PnP,
  author =       {Yinqiang Zheng and Yubin Kuang and Shigeki Sugimoto and Kalle Åström and Masatoshi Okutomi},
  booktitle =    {2013 IEEE International Conference on Computer Vision},
  title =        {Revisiting the PnP Problem: A Fast, General and Optimal Solution},
  year =         {2013},
  pages =        {2344--2351},
  keywords =     {computational complexity;image processing;minimisation;polynomials;Gr"obner basis technique;Grobner basis solver;PnP Problem;first noniterative O(n) solution;first-order optimality condition;functional minimization problem;perspective-n-point problem;polynomial system;two-fold symmetry;unconstrained optimization problem;Accuracy;Cameras;Minimization methods;Optimization;Polynomials;Quaternions;Three-dimensional displays},
  doi =          {10.1109/ICCV.2013.291},
  ISSN =         {1550-5499},
  month =        {December},
}

@ARTICLE{SGM,
  author =       {Heiko Hirschm\"uller},
  journal =      {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  title =        {Stereo Processing by Semiglobal Matching and Mutual Information},
  year =         {2008},
  volume =       {30},
  number =       {2},
  pages =        {328--341},
  keywords =     {image matching;image reconstruction;stereo image processing;3D reconstruction;multibaseline matching;mutual information based matching;occlusion detection;orthographic projection;pathwise optimization;pixelwise matching;radiometric transformation;semiglobal matching;stereo processing;subpixel refinement;global optimization;multi-baseline;mutual information;stereo},
  doi =          {10.1109/TPAMI.2007.1166},
  ISSN =         {0162-8828},
  month =        {February},
}

@ARTICLE{facial,
  author =       {Permenter, Frank and Parrilo, Pablo A.},
  title =        {Partial facial reduction: simplified, equivalent {SDP}s via approximations of the {PSD} cone},
  journal =      {ArXiv e-prints},
  archivePrefix ={arXiv},
  eprint =       {1408.4685},
  primaryClass = {math.OC},
  keywords =     {Mathematics - Optimization and Control},
  year =         {2014},
  month =        {August},
}

@ARTICLE{SDPstability,
  author =       {Cifuentes, Diego and Agarwal, Sameer and Parrilo, Pablo~A. and Thomas, Rekha~R.},
  title =        {On the local stability of semidefinite relaxations},
  journal =      {ArXiv e-prints},
  archivePrefix ={arXiv},
  eprint =       {1710.04287},
  primaryClass = {math.OC},
  keywords =     {Mathematics - Optimization and Control, Mathematics - Algebraic Geometry, 90C22 (Primary), 90C31 (Secondary)},
  year =         {2017},
  month =        {October},
}

@book{lasserre2015,
  title =        {An Introduction to Polynomial and Semi-Algebraic Optimization},
  author =       {Lasserre, Jean B.},
  series =       {Cambridge Texts in Applied Mathematics},
  year =         {2015},
  publisher =    {Cambridge University Press}
}

@BOOK{Bochnak-Coste-Roy98,
  author =       {Bochnak, Jacek and Coste, Michel and Roy, Marie-Fran{\c c}oise},
  title =        {Real Algebraic Geometry},
  volume =       {36},
  year =         {1998},
  pages =        {430},
  publisher =    {Springer},
  address =      {Berlin, Germany },
  edition =      {},
  series =       {Ergebnisse der Mathematik und ihrer Grenzgebiete},
}

@InProceedings{Larsson,
  author =       {Larsson, Viktor and Astrom, Kalle and Oskarsson, Magnus},
  title =        {Efficient Solvers for Minimal Problems by Syzygy-Based Reduction},
  booktitle =    {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
  month =        {July},
  year =         {2017}
}