Mixed-integer bilevel representability

[1]  Ted K. Ralphs,et al.  A branch-and-cut algorithm for mixed integer bilevel linear optimization problems and its implementation , 2020, Mathematical Programming Computation.

[2]  Andrew J. Schaefer,et al.  Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function , 2019, Oper. Res..

[3]  Alberto Del Pia,et al.  Characterizations of mixed binary convex quadratic representable sets , 2019, Math. Program..

[4]  F. You,et al.  A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs , 2017, Journal of Global Optimization.

[5]  Matteo Fischetti,et al.  On the use of intersection cuts for bilevel optimization , 2017, Mathematical Programming.

[6]  Alberto Del Pia,et al.  Ellipsoidal mixed-integer representability , 2018, Math. Program..

[7]  S. Sankaranarayanan Optimization with mixed-integer, complementarity and bilevel constraints with applications to energy and food markets , 2018 .

[8]  Matteo Fischetti,et al.  A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs , 2017, Oper. Res..

[9]  Pan Xu,et al.  The Watermelon Algorithm for The Bilevel Integer Linear Programming Problem , 2017, SIAM J. Optim..

[10]  Fengqi You,et al.  A Projection-Based Reformulation and Decomposition Algorithm for Global Optimization of Mixed Integer Bilevel Linear Programs , 2017 .

[11]  Ilias Zadik,et al.  Regularity in mixed-integer convex representability , 2017 .

[12]  Stephan Dempe,et al.  Solving discrete linear bilevel optimization problems using the optimal value reformulation , 2017, J. Glob. Optim..

[13]  Jonathan Cole Smith,et al.  A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem , 2017, Oper. Res..

[14]  Amitabh Basu,et al.  Mixed-Integer Linear Representability, Disjunctions, and Variable Elimination , 2016, IPCO.

[15]  Ilias Zadik,et al.  Mixed-Integer Convex Representability , 2016, IPCO.

[16]  Marco Molinaro,et al.  Mixed-integer quadratic programming is in NP , 2014, Mathematical Programming.

[17]  Russell Bent,et al.  Extended Formulations in Mixed-Integer Convex Programming , 2015, IPCO.

[18]  Massimiliano Caramia,et al.  Enhanced exact algorithms for discrete bilevel linear problems , 2015, Optim. Lett..

[19]  Juan Pablo Vielma,et al.  Mixed Integer Linear Programming Formulation Techniques , 2015, SIAM Rev..

[20]  Gerhard J. Woeginger,et al.  Bilevel programming and the separation problem , 2013, Mathematical Programming.

[21]  Gerhard J. Woeginger,et al.  A Study on the Computational Complexity of the Bilevel Knapsack Problem , 2014, SIAM J. Optim..

[22]  Santanu S. Dey,et al.  Some properties of convex hulls of integer points contained in general convex sets , 2013, Math. Program..

[23]  Jane J. Ye,et al.  New Necessary Optimality Conditions for Bilevel Programs by Combining the MPEC and Value Function Approaches , 2010, SIAM J. Optim..

[24]  M. Queyranne,et al.  Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs , 2009, 0907.1298.

[25]  R. Cottle Linear Complementarity Problem , 2009, Encyclopedia of Optimization.

[26]  Charles Audet,et al.  Disjunctive cuts for continuous linear bilevel programming , 2006, Optim. Lett..

[27]  M. Rao,et al.  Technical Report Integer Programming 1 Integer Programming 4 , 1998 .

[28]  Alexander Barvinok,et al.  A course in convexity , 2002, Graduate studies in mathematics.

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

[30]  J. Mirrlees The Theory of Moral Hazard and Unobservable Behaviour: Part I , 1999 .

[31]  Xiaotie Deng,et al.  Complexity Issues in Bilevel Linear Programming , 1998 .

[32]  Egon Balas,et al.  Gomory cuts revisited , 1996, Oper. Res. Lett..

[33]  Charles E. Blair A closed-form representation of mixed-integer program value functions , 1995, Math. Program..

[34]  Pierre Hansen,et al.  Links Between Linear Bilevel and Mixed 0–1 Programming Problems , 1995 .

[35]  L. N. Vicente,et al.  Discrete linear bilevel programming problem , 1996 .

[36]  J. Bard,et al.  An algorithm for the discrete bilevel programming problem , 1992 .

[37]  Jonathan F. Bard,et al.  The Mixed Integer Linear Bilevel Programming Problem , 1990, Oper. Res..

[38]  Robert G. Jeroslow,et al.  The polynomial hierarchy and a simple model for competitive analysis , 1985, Math. Program..

[39]  J. K. Lowe Modelling with Integer Variables. , 1984 .

[40]  Charles E. Blair,et al.  The value function of an integer program , 1982, Math. Program..

[41]  Wilfred Candler,et al.  A linear two-level programming problem, , 1982, Comput. Oper. Res..

[42]  Charles E. Blair,et al.  The value function of a mixed integer program: II , 1979, Discret. Math..

[43]  Robert G. Jeroslow,et al.  Some Basis Theorems for Integral Monoids , 1978, Math. Oper. Res..

[44]  Charles E. Blair,et al.  The value function of a mixed integer program: I , 1977, Discret. Math..

[45]  R. Rockafellar Convex Analysis: (pms-28) , 1970 .