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## A lifted linear programming branch-and-bound algorithm for mixed integer conic quadratic programs (2007)

Citations: | 26 - 1 self |

### Citations

370 | Adjustable robust solutions of uncertain linear programs - Ben-Tal, Goryashko, et al. - 2004 |

226 |
Generalized Benders decomposition
- Geoffrion
- 1972
(Show Context)
Citation Context ... procedure or as a local search procedure. Some of the algorithms in this group include outer approximation (Duran and Grossmann, 1986; Fletcher and Leyffer, 1994), generalized Benders decomposition (=-=Geoffrion, 1972-=-), LP/NLP-based branch-and-bound (Quesada and Grossmann, 1992) and the extended cutting plane method (Westerlund and Pettersson, 1995; Westerlund et al., 1994). This approach is the basis for the I-OA... |

215 | Applications of second-order cone programming
- Lobo, Vandenberghe, et al.
- 1998
(Show Context)
Citation Context ...r programming (MINLP) problems known as mixed integer conic quadratic programming problems. This class of problems arises from adding integrality requirements to conic quadratic programming problems (=-=Lobo et al., 1998-=-), and is used to model several applications from engineering and finance. Conic quadratic programming problems are also known as second order cone programming problems, and together with semidefinite... |

209 |
An outer-approximation algorithm for a class of mixed-integer nonlinear programs
- Duran, Grossmann
- 1986
(Show Context)
Citation Context ...ble solutions, to improve the polyhedral relaxations, to fathom nodes in a branch-and-bound procedure or as a local search procedure. Some of the algorithms in this group include outer approximation (=-=Duran and Grossmann, 1986-=-; Fletcher and Leyffer, 1994), generalized Benders decomposition (Geoffrion, 1972), LP/NLP-based branch-and-bound (Quesada and Grossmann, 1992) and the extended cutting plane method (Westerlund and Pe... |

171 | An elementary introduction to modern convex geometry
- Ball
- 1997
(Show Context)
Citation Context ...e nonlinear constraints. In particular, it is known that obtaining a tight polyhedral approximation of the Euclidean ball without using extra variables requires an exponential number of inequalities (=-=Ball, 1997-=-). To try to resolve this issue, current polyhedral based algorithms generate the relaxations dynamically. In the context of CP problems, an alternative polyhedral relaxation that is not based on grad... |

110 | An algorithmic framework for convex mixed integer nonlinear programs.
- Bonami, Biegler, et al.
- 2008
(Show Context)
Citation Context ... of the LP based branch-and-bound procedure for mixed integer linear programming (MILP) problems and is the basis for the MICP solver in CPLEX 9.0 and 10.0 (ILOG, 2005) and the I-BB solver in Bonmin (=-=Bonami et al., 2005-=-). We refer to these algorithms as NLP based branch-and-bound algorithms. The second group uses polyhedral relaxations of the nonlinear constraints of MICPP, possibly together with the nonlinear relax... |

99 | Heuristics for cardinality constrained portfolio optimization. - Chang, Meade, et al. - 2000 |

94 | Review of nonlinear mixed-integer and disjunctive programming techniques,” - Grossmann - 2002 |

86 | Solving mixed integer nonlinear programs by outer approximation
- Fletcher, Leyffer
- 1994
(Show Context)
Citation Context ...he polyhedral relaxations, to fathom nodes in a branch-and-bound procedure or as a local search procedure. Some of the algorithms in this group include outer approximation (Duran and Grossmann, 1986; =-=Fletcher and Leyffer, 1994-=-), generalized Benders decomposition (Geoffrion, 1972), LP/NLP-based branch-and-bound (Quesada and Grossmann, 1992) and the extended cutting plane method (Westerlund and Pettersson, 1995; Westerlund e... |

73 |
A cutting plane method for solving con- vex MINLP problems
- Westerlund, Pettersson
- 1995
(Show Context)
Citation Context ...d Grossmann, 1986; Fletcher and Leyffer, 1994), generalized Benders decomposition (Geoffrion, 1972), LP/NLP-based branch-and-bound (Quesada and Grossmann, 1992) and the extended cutting plane method (=-=Westerlund and Pettersson, 1995-=-; Westerlund et al., 1994). This approach is the basis for the I-OA, I-QG and I-Hyb solvers in Bonmin (Bonami et al., 2005) and the MINLP solver FilMINT (Abhishek et al., 2006). We refer to these algo... |

72 |
An LP/NLP based branch and bound al- gorithm for convex MINLP optimization problems
- Quesada, Grossman
- 1992
(Show Context)
Citation Context ...f the algorithms in this group include outer approximation (Duran and Grossmann, 1986; Fletcher and Leyffer, 1994), generalized Benders decomposition (Geoffrion, 1972), LP/NLP-based branch-and-bound (=-=Quesada and Grossmann, 1992-=-) and the extended cutting plane method (Westerlund and Pettersson, 1995; Westerlund et al., 1994). This approach is the basis for the I-OA, I-QG and I-Hyb solvers in Bonmin (Bonami et al., 2005) and ... |

72 |
A branch-and-cut method for 0–1 mixed convex programming.
- Stubbs, Mehrotra
- 1999
(Show Context)
Citation Context ...ami et al. (2005) and Grossmann (2002)). The first group only uses the nonlinear relaxation CPP in a branch-and-bound procedure (Borchers and Mitchell, 1994; Gupta and Ravindran, 1985; Leyffer, 2001; =-=Stubbs and Mehrotra, 1999-=-). This procedure is the direct analog of the LP based branch-and-bound procedure for mixed integer linear programming (MILP) problems and is the basis for the MICP solver in CPLEX 9.0 and 10.0 (ILOG,... |

71 | Portfolio optimization with linear and fixed transaction costs. - Lobo, Fazel, et al. - 2007 |

69 | Computational study of a family of mixed-integer quadratic programming problems. - Bienstock - 1995 |

64 | FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs.
- Abhishek, Leyffer, et al.
- 2010
(Show Context)
Citation Context ... plane method (Westerlund and Pettersson, 1995; Westerlund et al., 1994). This approach is the basis for the I-OA, I-QG and I-Hyb solvers in Bonmin (Bonami et al., 2005) and the MINLP solver FilMINT (=-=Abhishek et al., 2006-=-). We refer to these algorithms as polyhedral relaxation based algorithms. For algorithms in the second group to perform efficiently, it is essential to have polyhedral relaxations of the nonlinear co... |

60 |
Branch and bound experiments in convex non- linear integer programming
- Gupta, Ravindran
- 1985
(Show Context)
Citation Context ... relaxations they use (see for example Bonami et al. (2005) and Grossmann (2002)). The first group only uses the nonlinear relaxation CPP in a branch-and-bound procedure (Borchers and Mitchell, 1994; =-=Gupta and Ravindran, 1985-=-; Leyffer, 2001; Stubbs and Mehrotra, 1999). This procedure is the direct analog of the LP based branch-and-bound procedure for mixed integer linear programming (MILP) problems and is the basis for th... |

48 | An improved branch and bound algorithm for mixed integer nonlinear programs
- Borchers, Mitchell
- 1994
(Show Context)
Citation Context ...ng on what type of continuous relaxations they use (see for example Bonami et al. (2005) and Grossmann (2002)). The first group only uses the nonlinear relaxation CPP in a branch-and-bound procedure (=-=Borchers and Mitchell, 1994-=-; Gupta and Ravindran, 1985; Leyffer, 2001; Stubbs and Mehrotra, 1999). This procedure is the direct analog of the LP based branch-and-bound procedure for mixed integer linear programming (MILP) probl... |

45 | Integrating SQP and branch-and-bound for mixed integer nonlinear programming - Leyffer - 1998 |

24 |
Incorporating estimation errors in portfolio selection: Robust portfolio construction,"
- Ceria, Stubbs
- 2006
(Show Context)
Citation Context ...raints of LPP and the integrality of the x variables. 12s4.2. Test Instances Our test set consists of three different portfolio optimization problems with cardinality constraints from the literature (=-=Ceria and Stubbs, 2006-=-; Lobo et al., 1998, 2007). For most portfolio optimization problems only the continuous variables are present in the nonlinear constraints and hence the convex hull of integer feasible solutions to t... |

19 | Optimization of Cardinality Constrained Portfolios with an Hybrid Local Search Algorithm”. - Kellerer, Maringer - 2001 |

12 | 2002. Benchmarking optimization software with performance profiles - Dolan, More |

6 | Computational experiments with a linear approximation of second-order cone optimization. Faculté Polytechnique de - Glineur - 2000 |

2 | An algorithm for cardinality constrained quadratic optimization problems. Working Paper, http://web.mit.edu/dbertsim/www/papers.html - Bertsimas, Shioda - 2004 |

1 | Lectures on modern convex optimization: analysis, algorithms, and engineering applications - 2001a |

1 | On polyhedral approximations of the second-order cone - 2001b |