Foundations of Discrete Optimization: In Transition from Linear to Non-linear Models and Methods

[1]  Jesús A. De Loera,et al.  Algebraic and Geometric Ideas in the Theory of Discrete Optimization , 2012, MOS-SIAM Series on Optimization.

[2]  Matthias Köppe,et al.  A new Lenstra-type algorithm for quasiconvex polynomial integer minimization with complexity 2O(nlogn) , 2010, Discret. Optim..

[3]  Jesús A. De Loera,et al.  Transportation Problems and Simplicial Polytopes That Are Not Weakly Vertex-Decomposable , 2012, Math. Oper. Res..

[4]  R. Weismantel,et al.  Convex integer minimization in fixed dimension , 2012, 1203.4175.

[5]  Jesús A. De Loera,et al.  The Central Curve in Linear Programming , 2010, Found. Comput. Math..

[6]  W. W. Adams,et al.  An Introduction to Gröbner Bases , 2012 .

[7]  Santosh S. Vempala,et al.  Enumerative Lattice Algorithms in any Norm Via M-ellipsoid Coverings , 2010, 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science.

[8]  Raymond Hemmecke,et al.  A polynomial oracle-time algorithm for convex integer minimization , 2007, Math. Program..

[9]  S. Onn.  Nonlinear Discrete Optimization , 2010 .

[10]  Francisco Santos,et al.  A counterexample to the Hirsch conjecture , 2010, ArXiv.

[11]  Raymond Hemmecke,et al.  A Polynomial-Time Algorithm for Optimizing over N-Fold 4-Block Decomposable Integer Programs , 2009, IPCO.

[12]  Edward D. Kim,et al.  An Update on the Hirsch Conjecture , 2009, 0907.1186.

[13]  O. Schnetz.  Quantum periods : A census of φ 4-transcendentals , 2010 .

[14]  M. Jünger,et al.  50 Years of Integer Programming 1958-2008 - From the Early Years to the State-of-the-Art , 2010 .

[15]  Alexander A. Razborov,et al.  Diameter of polyhedra: limits of abstraction , 2009, SCG '09.

[16]  Tamás Terlaky,et al.  A Continuous d-Step Conjecture for Polytopes , 2009, Discret. Comput. Geom..

[17]  Shu Lin,et al.  Applied Algebra, Algebraic Algorithms and Error-Correcting Codes , 1999, Lecture Notes in Computer Science.

[18]  Hanif D. Sherali,et al.  Advances in Applied Mathematics and Global Optimization , 2009 .

[19]  Tamás Terlaky,et al.  Central Path Curvature and Iteration-Complexity for Redundant Klee—Minty Cubes , 2009 .

[20]  Takashi Tsuchiya,et al.  A strong bound on the integral of the central path curvature and its relationship with the iteration-complexity of primal-dual path-following LP algorithms , 2008, Math. Program..

[21]  Tamás Terlaky,et al.  Polytopes and arrangements: Diameter and curvature , 2008, Oper. Res. Lett..

[22]  S. Sullivant,et al.  A finiteness theorem for Markov bases of hierarchical models , 2004, J. Comb. Theory, Ser. A.

[23]  D. Kreimer,et al.  On Motives Associated to Graph Polynomials , 2005, math/0510011.

[24]  J. D. Loera,et al.  Integer Polynomial Optimization in Fixed Dimension , 2004, Math. Oper. Res..

[25]  C. Roos,et al.  Interior Point Methods for Linear Optimization , 2005 .

[26]  Sebastian Heinz,et al.  Complexity of integer quasiconvex polynomial optimization , 2005, J. Complex..

[27]  Michael Shub,et al.  On the Curvature of the Central Path of Linear Programming Theory , 2003, Found. Comput. Math..

[28]  B. Sturmfels,et al.  Higher Lawrence configurations , 2002, J. Comb. Theory, Ser. A.

[29]  A. Barvinok,et al.  Short rational generating functions for lattice point problems , 2002, math/0211146.

[30]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[31]  Leonid Khachiyan,et al.  Integer Optimization on Convex Semialgebraic Sets , 2000, Discret. Comput. Geom..

[32]  A. Connes,et al.  Renormalization in Quantum Field Theory and the Riemann--Hilbert Problem II: The β-Function, Diffeomorphisms and the Renormalization Group , 1999, hep-th/9909126.

[33]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[34]  Louis J. Billera,et al.  New perspectives in algebraic combinatorics , 1999 .

[35]  A. Barvinok,et al.  An Algorithmic Theory of Lattice Points in Polyhedra , 1999 .

[36]  Rekha R. Thomas,et al.  Gröbner Bases and Applications: Gröbner Bases and Integer Programming , 1998 .

[37]  B. Buchberger,et al.  Gröbner bases and applications , 1998 .

[38]  Robert J. Vanderbei,et al.  Linear Programming: Foundations and Extensions , 1998, Kluwer international series in operations research and management service.

[39]  William J. Cook,et al.  Combinatorial optimization , 1997 .

[40]  Martin E. Dyer,et al.  On Barvinok's Algorithm for Counting Lattice Points in Fixed Dimension , 1997, Math. Oper. Res..

[41]  Yinyu Ye,et al.  A primal-dual interior point method whose running time depends only on the constraint matrix , 1996, Math. Program..

[42]  D. Broadhurst,et al.  Beyond the triangle and uniqueness relations: non-zeta counterterms at large N from positive knots , 1996, hep-th/9607174.

[43]  Rekha R. Thomas.  A Geometric Buchberger Algorithm for Integer Programming , 1995, Math. Oper. Res..

[44]  S. D. Chatterji.  Proceedings of the International Congress of Mathematicians , 1995 .

[45]  G. Ziegler.  Lectures on Polytopes , 1994 .

[46]  Alexander I. Barvinok,et al.  A polynomial time algorithm for counting integral points in polyhedra when the dimension is fixed , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[47]  J. Stoer,et al.  Estimating the complexity of a class of path-following methods for solving linear programs by curvature integrals , 1993 .

[48]  David A. Cox,et al.  Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics) , 2007 .

[49]  Gil Kalai.  Upper bounds for the diameter and height of graphs of convex polyhedra , 1992, Discret. Comput. Geom..

[50]  W. Kern,et al.  Linear Programming Duality: An Introduction to Oriented Matroids , 1992 .

[51]  G. Kalai,et al.  A quasi-polynomial bound for the diameter of graphs of polyhedra , 1992, math/9204233.

[52]  V. Emelichev,et al.  On cardinality of the set of alternatives in discrete many-criterion problems , 1992 .

[53]  Josef Stoer,et al.  On the complexity of following the central path of linear programs by linear extrapolation II , 1991, Math. Program..

[54]  Carlo Traverso,et al.  Buchberger Algorithm and Integer Programming , 1991, AAECC.

[55]  D. Bayer,et al.  The nonlinear geometry of linear programming. II. Legendre transform coordinates and central trajectories , 1989 .

[56]  D. Bayer,et al.  The Non-Linear Geometry of Linear Pro-gramming I: A?ne and projective scaling trajectories , 1989 .

[57]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1988, Algorithms and Combinatorics.

[58]  M. Brion.  Points entiers dans les polyèdres convexes , 1988 .

[59]  Victor Klee,et al.  The d-Step Conjecture and Its Relatives , 1987, Math. Oper. Res..

[60]  I. Sergienko,et al.  Finding the set of alternatives in discrete multicriterion problems , 1987 .

[61]  András Frank,et al.  An application of simultaneous diophantine approximation in combinatorial optimization , 1987, Comb..

[62]  R. Stanley.  What Is Enumerative Combinatorics , 1986 .

[63]  Willard Miller,et al.  The IMA volumes in mathematics and its applications , 1986 .

[64]  Hendrik W. Lenstra,et al.  Integer Programming with a Fixed Number of Variables , 1983, Math. Oper. Res..

[65]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[66]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[67]  J. Scott Provan,et al.  Decompositions of Simplicial Complexes Related to Diameters of Convex Polyhedra , 1980, Math. Oper. Res..

[68]  David W. Walkup,et al.  A 3-Sphere Counterexample to the Wv-Path Conjecture , 1980, Math. Oper. Res..

[69]  L. Khachiyan.  Polynomial algorithms in linear programming , 1980 .

[70]  Heinz Isermann,et al.  Technical Note - Proper Efficiency and the Linear Vector Maximum Problem , 1974, Oper. Res..

[71]  G. Dantzig,et al.  Maximum Diameter of Abstract Polytopes , 1974 .

[72]  K. G. Murty,et al.  Existence of A-avoiding paths in abstract polytopes , 1974 .

[73]  David W. Barnette.  An upper bound for the diameter of a polytope , 1974, Discret. Math..

[74]  D. Larman.  Paths on Polytopes , 1970 .