Mathematical Programming Computation, ISSN 1867-2949, 6/2011, Volume 3, Issue 2, pp. 103 - 163

This paper reports on the fifth version of the Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a...

90C10 | MIP | Operations Research/Decision Theory | Problem instances | 90C11 | 90C90 | Mathematics | Mixed Integer Programming | Optimization | MIPLIB | Mixed integer programming

90C10 | MIP | Operations Research/Decision Theory | Problem instances | 90C11 | 90C90 | Mathematics | Mixed Integer Programming | Optimization | MIPLIB | Mixed integer programming

Journal Article

The Annals of Statistics, ISSN 0090-5364, 4/2016, Volume 44, Issue 2, pp. 813 - 852

In the period 1991-2015, algorithmic advances in Mixed Integer Optimization (MIO) coupled with hardware improvements have resulted in an astonishing 450...

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Datasets | Integers | Regression coefficients | Optimal solutions | Statistical properties | Linear regression | Threshing | Correlation coefficients | Least squares | Predictive modeling | Best subset selection | Global optimization | Algorithms | Lasso | Sparse linear regression | Least absolute deviation | Discrete optimization | Mixed integer programming | ℓ0-constrained minimization | l-constrained minimization | SPARSITY | algorithms | lasso | PERSISTENCE | STATISTICS & PROBABILITY | VARIABLE SELECTION | global optimization | NONCONCAVE PENALIZED LIKELIHOOD | RECOVERY | least absolute deviation | mixed integer programming | discrete optimization | REGRESSION SHRINKAGE | best subset selection | 62J05 | 62J07 | 90C26 | 90C27 | ell_{0}-constrained minimization | 90C11 | 62G35

Journal Article

Mathematical Programming, ISSN 0025-5610, 2018, Volume 179, Issue 1-2, pp. 455 - 468

A classic result of Cook et al. (Math. Program. 34:251-264, 1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | 11B75 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROXIMITY | 90C11 | Linear programming | Combinatorial analysis | Number theory | Linear functions | Integers

COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | 11B75 | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | PROXIMITY | 90C11 | Linear programming | Combinatorial analysis | Number theory | Linear functions | Integers

Journal Article

Mathematical Programming, ISSN 0025-5610, 6/2011, Volume 128, Issue 1, pp. 49 - 72

Many combinatorial constraints over continuous variables such as SOS1 and SOS2 constraints can be interpreted as disjunctive constraints that restrict the...

Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | 90C26 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PIECEWISE-LINEAR OPTIMIZATION | REPRESENTABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FORMULATIONS | COMBINATORIAL OPTIMIZATION | ALGORITHM | CONVEX-HULL | NONCONVEX | INTEGER PROGRAMMING-MODELS | BRANCH-AND-CUT | Studies | Graphs | Mathematical analysis | Mixed integer | Polyhedra | Polyhedrons | Mathematical models | Tightness | Combinatorial analysis | Unions

Mathematical Methods in Physics | Mathematics of Computing | Calculus of Variations and Optimal Control; Optimization | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | 90C26 | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PIECEWISE-LINEAR OPTIMIZATION | REPRESENTABILITY | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | FORMULATIONS | COMBINATORIAL OPTIMIZATION | ALGORITHM | CONVEX-HULL | NONCONVEX | INTEGER PROGRAMMING-MODELS | BRANCH-AND-CUT | Studies | Graphs | Mathematical analysis | Mixed integer | Polyhedra | Polyhedrons | Mathematical models | Tightness | Combinatorial analysis | Unions

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 4/2019, Volume 73, Issue 4, pp. 789 - 800

The tensor complementarity problem is a special instance of nonlinear complementarity problems, which has many applications. How to solve the tensor...

Unique solution | Operations Research/Decision Theory | 90C11 | Tensor complementarity problem | Positive definite | Mixed integer programming | Mathematics | 15A69 | Computer Science, general | Optimization | Real Functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Integer programming | Mixed integer | Tensors | Mathematical analysis

Unique solution | Operations Research/Decision Theory | 90C11 | Tensor complementarity problem | Positive definite | Mixed integer programming | Mathematics | 15A69 | Computer Science, general | Optimization | Real Functions | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Integer programming | Mixed integer | Tensors | Mathematical analysis

Journal Article

Mathematical Programming, ISSN 0025-5610, 5/2016, Volume 157, Issue 1, pp. 47 - 67

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs....

Lower bounding | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Stochastic mixed-integer programming | 90C15 Stochastic Programming | 90C11 Mixed Integer Programming | Mathematics | Decomposition algorithms | Combinatorics | UNIT COMMITMENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTERDICTION | DUAL DECOMPOSITION | MODEL | Algorithms | Studies | Operations research | Mathematical models | Mathematical programming | Lower bounds | Site selection | Computation | Mathematical analysis | Unit commitment | Stochasticity | Standards | decomposition algorithms | MATHEMATICS AND COMPUTING | stochastic mixed-integer programming | lower bounding

Lower bounding | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Stochastic mixed-integer programming | 90C15 Stochastic Programming | 90C11 Mixed Integer Programming | Mathematics | Decomposition algorithms | Combinatorics | UNIT COMMITMENT | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTERDICTION | DUAL DECOMPOSITION | MODEL | Algorithms | Studies | Operations research | Mathematical models | Mathematical programming | Lower bounds | Site selection | Computation | Mathematical analysis | Unit commitment | Stochasticity | Standards | decomposition algorithms | MATHEMATICS AND COMPUTING | stochastic mixed-integer programming | lower bounding

Journal Article

Mathematical Programming, ISSN 0025-5610, 8/2014, Volume 146, Issue 1, pp. 219 - 244

We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with finite support and random polyhedral...

Probabilistic constraints | Theoretical, Mathematical and Computational Physics | Chance constraints | Mathematics | Decomposition | 90C15 | Stochastic programming | Integer programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Combinatorics | MATHEMATICS, APPLIED | DISCRETE-DISTRIBUTIONS | EQUIVALENTS | CONVEX APPROXIMATIONS | STRATEGIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | OPTIMIZATION | LINEAR-PROGRAMS | Call centers | Call center software | Algorithms | Studies | Stochastic models | Analysis | Risk levels | Mathematical analysis | Inequalities | Programming | Mathematical models

Probabilistic constraints | Theoretical, Mathematical and Computational Physics | Chance constraints | Mathematics | Decomposition | 90C15 | Stochastic programming | Integer programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Combinatorics | MATHEMATICS, APPLIED | DISCRETE-DISTRIBUTIONS | EQUIVALENTS | CONVEX APPROXIMATIONS | STRATEGIES | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | MODELS | OPTIMIZATION | LINEAR-PROGRAMS | Call centers | Call center software | Algorithms | Studies | Stochastic models | Analysis | Risk levels | Mathematical analysis | Inequalities | Programming | Mathematical models

Journal Article

Mathematical Programming, ISSN 0025-5610, 5/2019, Volume 175, Issue 1, pp. 461 - 502

Multistage stochastic integer programming (MSIP) combines the difficulty of uncertainty, dynamics, and non-convexity, and constitutes a class of extremely...

Theoretical, Mathematical and Computational Physics | Nested decomposition | 90C39 | Mathematics | Multistage stochastic integer programming | 90C15 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Binary state variables | Stochastic dual dynamic programming | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECOMPOSITION | OPTIMIZATION | MODEL | NETWORK REVENUE MANAGEMENT | Portfolio management | Algorithms | Electric power production | Integer programming | Multistage | Benders decomposition | Financial management | Tightness | Dynamic programming | Convexity | Linear functions

Theoretical, Mathematical and Computational Physics | Nested decomposition | 90C39 | Mathematics | Multistage stochastic integer programming | 90C15 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | 90C11 | Binary state variables | Stochastic dual dynamic programming | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | DECOMPOSITION | OPTIMIZATION | MODEL | NETWORK REVENUE MANAGEMENT | Portfolio management | Algorithms | Electric power production | Integer programming | Multistage | Benders decomposition | Financial management | Tightness | Dynamic programming | Convexity | Linear functions

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2018, Volume 172, Issue 1, pp. 139 - 168

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen...

Convex MINLP | Theoretical, Mathematical and Computational Physics | Mathematics | Disciplined convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90–08 | 90C25 | Numerical Analysis | 90C11 | Outer approximation | Combinatorics | BRANCH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NONLINEAR PROGRAMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SOFTWARE | Analysis | Algorithms | Computational geometry | Solvers | Modelling | Convexity | Convex analysis | Optimization | Mathematical programming | Mathematics - Optimization and Control

Convex MINLP | Theoretical, Mathematical and Computational Physics | Mathematics | Disciplined convex programming | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90–08 | 90C25 | Numerical Analysis | 90C11 | Outer approximation | Combinatorics | BRANCH | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | NONLINEAR PROGRAMS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SOFTWARE | Analysis | Algorithms | Computational geometry | Solvers | Modelling | Convexity | Convex analysis | Optimization | Mathematical programming | Mathematics - Optimization and Control

Journal Article

Mathematical Programming, ISSN 0025-5610, 5/2019, Volume 175, Issue 1, pp. 197 - 240

This paper investigates a polyhedral approach to handle symmetries in mixed-binary programs. We study symretopes, i.e., the convex hulls of all binary vectors...

Mathematical Methods in Physics | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | Combinatorics | 90C09 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Integer programming | Polytopes | Computational geometry | Binary stars | Hulls (structures) | Convexity | Hulls | Symmetry

Mathematical Methods in Physics | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Theoretical, Mathematical and Computational Physics | 90C11 | Mathematics | Combinatorics | 90C09 | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Integer programming | Polytopes | Computational geometry | Binary stars | Hulls (structures) | Convexity | Hulls | Symmetry

Journal Article

Mathematical Programming Computation, ISSN 1867-2949, 3/2012, Volume 4, Issue 1, pp. 1 - 31

We propose two primal heuristics for nonconvex mixed-integer nonlinear programs. Both are based on the idea of rounding the solution of a continuous nonlinear...

Mathematics | 90C59 | 90C57 | Operations Research/Decision Theory | 90C11 | Optimization

Mathematics | 90C59 | 90C57 | Operations Research/Decision Theory | 90C11 | Optimization

Journal Article

Computational Geosciences, ISSN 1420-0597, 8/2014, Volume 18, Issue 3, pp. 463 - 482

In oil field development, the optimal location for a new well depends on how it is to be operated. Thus, it is generally suboptimal to treat the well location...

Field development optimization | Production optimization | Earth Sciences | 90-08 | Geotechnical Engineering & Applied Earth Sciences | Earth Sciences, general | 90C26 | Derivative-free optimization | Hydrogeology | 90C30 | 90C11 | 90C56 | Well placement | 90C90 | Mathematical Modeling and Industrial Mathematics | Nonlinear programming | Reservoir simulation-based optimization | Soil Science & Conservation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSCIENCES, MULTIDISCIPLINARY | ALGORITHMS | PLACEMENT OPTIMIZATION | Oil fields | Algorithms | Mathematical optimization | Methods | Optimization algorithms | Wells | Geoengineering | Computation | Searching | Control equipment | Nonlinearity | Mathematical models | Swarm intelligence | Optimization

Field development optimization | Production optimization | Earth Sciences | 90-08 | Geotechnical Engineering & Applied Earth Sciences | Earth Sciences, general | 90C26 | Derivative-free optimization | Hydrogeology | 90C30 | 90C11 | 90C56 | Well placement | 90C90 | Mathematical Modeling and Industrial Mathematics | Nonlinear programming | Reservoir simulation-based optimization | Soil Science & Conservation | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | GEOSCIENCES, MULTIDISCIPLINARY | ALGORITHMS | PLACEMENT OPTIMIZATION | Oil fields | Algorithms | Mathematical optimization | Methods | Optimization algorithms | Wells | Geoengineering | Computation | Searching | Control equipment | Nonlinearity | Mathematical models | Swarm intelligence | Optimization

Journal Article

Mathematical Programming Computation, ISSN 1867-2949, 12/2011, Volume 3, Issue 4, pp. 349 - 390

Finding good (or even just feasible) solutions for Mixed-Integer Nonlinear Programming problems independently of the specific problem structure is a very hard...

Mathematics | 90C26 | 90C59 | Operations Research/Decision Theory | 90C11 | Optimization

Mathematics | 90C26 | 90C59 | Operations Research/Decision Theory | 90C11 | Optimization

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2019, Volume 177, Issue 1, pp. 371 - 394

Representability results play a fundamental role in optimization since they provide characterizations of the feasible sets that arise from optimization...

Theoretical, Mathematical and Computational Physics | Mathematics | Quadratic programming | 90C20 | 90C10 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Mixed-integer programming | 90C11 | Convex functions | Representability | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Economic models | Continuity (mathematics) | Optimization | Feasibility studies

Theoretical, Mathematical and Computational Physics | Mathematics | Quadratic programming | 90C20 | 90C10 | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Mixed-integer programming | 90C11 | Convex functions | Representability | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Economic models | Continuity (mathematics) | Optimization | Feasibility studies

Journal Article

Mathematical Programming Computation, ISSN 1867-2949, 9/2014, Volume 6, Issue 3, pp. 255 - 279

The feasibility pump (FP) has proved to be an effective method for finding feasible solutions to mixed integer programming problems. FP iterates between a...

90C10 | 65K05 | Mathematics of Computing | Operations Research/Decision Theory | 90C11 | Mathematics | Theory of Computation | Optimization

90C10 | 65K05 | Mathematics of Computing | Operations Research/Decision Theory | 90C11 | Mathematics | Theory of Computation | Optimization

Journal Article

Mathematical Programming, ISSN 0025-5610, 9/2019, Volume 177, Issue 1, pp. 21 - 53

There is often a significant trade-off between formulation strength and size in mixed integer programming. When modeling convex disjunctive constraints (e.g....

Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Mixed integer programming formulations | 90C11 | Disjunctive constraints | Mixed integer nonlinear programming | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTEGER NONLINEAR PROGRAMS | Analysis | Business schools | Integer programming | Polytopes | Mixed integer | Formulations | Computational geometry | Tradeoffs | Constraint modelling | Embedding | Convexity | Continuity (mathematics) | Unions

Theoretical, Mathematical and Computational Physics | Mathematics | Mathematical Methods in Physics | 90C30 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | 90C25 | Numerical Analysis | Mixed integer programming formulations | 90C11 | Disjunctive constraints | Mixed integer nonlinear programming | Combinatorics | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTEGER NONLINEAR PROGRAMS | Analysis | Business schools | Integer programming | Polytopes | Mixed integer | Formulations | Computational geometry | Tradeoffs | Constraint modelling | Embedding | Convexity | Continuity (mathematics) | Unions

Journal Article

Mathematical Programming, ISSN 0025-5610, 7/2016, Volume 158, Issue 1, pp. 175 - 205

We give strong formulations of ramping constraints—used to model the maximum change in production level for a generator or machine from one time period to the...

Polytope | Co-generation | Facets | Theoretical, Mathematical and Computational Physics | Unit commitment | Ramping | Mathematics | Valid inequalities | Mathematical Methods in Physics | Convex hull | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Production smoothing | Computation | Numerical Analysis | 90C11 | Combinatorics | MATHEMATICS, APPLIED | ALGORITHM | UNIT COMMITMENT PROBLEMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Cogeneration power plants | Management science | Algorithms | Electric power production | Analysis | Studies | Production management | Operations research | Mathematical models | Polynomials | Mathematical programming | MATHEMATICS AND COMPUTING | unit commitment | production smoothing, convex hull | co-generation | valid inequalities | polytope | facets | computation

Polytope | Co-generation | Facets | Theoretical, Mathematical and Computational Physics | Unit commitment | Ramping | Mathematics | Valid inequalities | Mathematical Methods in Physics | Convex hull | 90C57 | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Production smoothing | Computation | Numerical Analysis | 90C11 | Combinatorics | MATHEMATICS, APPLIED | ALGORITHM | UNIT COMMITMENT PROBLEMS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Cogeneration power plants | Management science | Algorithms | Electric power production | Analysis | Studies | Production management | Operations research | Mathematical models | Polynomials | Mathematical programming | MATHEMATICS AND COMPUTING | unit commitment | production smoothing, convex hull | co-generation | valid inequalities | polytope | facets | computation

Journal Article