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From Mixed-Integer Linear to Mixed-Integer Bilevel Linear Programming
2017Bilevel Optimization is a very challenging framework where two players (with different objectives) compete for the definition of the final solution. In this paper we address a generic mixed-integer bilevel linear program, i.e., a bilevel optimization problem where the objective functions and constraints are all linear, and some variables are required ...
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Guaranteed Outlier Removal with Mixed Integer Linear Programs
2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2016The maximum consensus problem is fundamentally important to robust geometric fitting in computer vision. Solving the problem exactly is computationally demanding, and the effort required increases rapidly with the problem size. Although randomized algorithms are much more efficient, the optimality of the solution is not guaranteed.
Tat-Jun Chin +3 more
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Marginal values in mixed integer linear programming
Mathematical Programming, 1989Marginal values of a given optimization problem are the directional partial derivatives of the value with respect to perturbations in the data. If \(v(c,A,b)=\min \{cx|\) Ax\(\geq b\), \(x\geq 0\}\) and if \(u=(c',A',b')\) is a vector, then the marginal value in direction u is defined by \[ \frac{\partial v}{\partial u}=\lim_{\epsilon \to 0+}\frac{v(c+\
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Linear and Mixed Integer Programming
2000Linear Programming (LP) is one of the most famous optimization techniques introduced independently by Kantarowitsch in 1939 and by Dantzig in 1949 (Kreko, 1973). LP is applicable in decision situations where quantities (variables) can take any real values only restricted by linear (in-) equalities, e. g. for representing capacity constraints. Still, LP
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Linear and Mixed Integer Programming for Portfolio Optimization
2015This book presents solutions to the general problem of single period portfolio optimization. It introduces different linear models, arising from different performance measures, and the mixed integer linear models resulting from the introduction of real features.
MANSINI, Renata +2 more
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Generative Branching for Mixed-Integer Linear Programming
Proceedings of the AAAI Conference on Artificial IntelligenceBranch-and-bound (B&B) is a fundamental algorithmic framework for solving Mixed-Integer Linear Programming (MILP) problems, where branching decisions critically affect solver efficiency. Recent learning-based methods apply imitation learning to select branching variables, but their deterministic predictions limit exploration and generalization.
Ruobing Wang +4 more
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Integer and Mixed Integer Linear Fractional Programming
1997Some of the problems mentioned in Chapter 1 required that either part of the variables, or all of them take integer values. This chapter will study such problems. In particular, we will address the bivalent programming in which part of the variables or all of them can take only values 0 or 1 (Section 9.1).
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Testing copositivity via mixed–integer linear programming
Linear Algebra and its Applications, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Valid Linear Programming Bounds for Exact Mixed-Integer Programming
INFORMS Journal on Computing, 2013Fast computation of valid linear programming (LP) bounds serves as an important subroutine for solving mixed-integer programming problems exactly. We introduce a new method for computing valid LP bounds designed for this application. The algorithm corrects approximate LP dual solutions to be exactly feasible, giving a valid bound.
Daniel E. Steffy, Kati Wolter
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Mixed integer linear programming formulations for probabilistic constraints
Operations Research Letters, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Juan Pablo Vielma +2 more
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