# Valid inequalities for separable concave constraints with indicator variables

@article{Lim2016ValidIF, title={Valid inequalities for separable concave constraints with indicator variables}, author={Cong Han Lim and Jeff T. Linderoth and James R. Luedtke}, journal={Mathematical Programming}, year={2016}, volume={172}, pages={415-442} }

We study valid inequalities for optimization models that contain both binary indicator variables and separable concave constraints. These models reduce to a mixed-integer linear program (MILP) when the concave constraints are ignored, or to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms designed to solve these problems to global optimality, cutting planes to strengthen the relaxation are traditionally obtained using valid inequalities for the…

## One Citation

### 2x2 convexifications for convex quadratic optimization with indicator variables

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- 2020

In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and…

## References

SHOWING 1-10 OF 43 REFERENCES

### On Valid Inequalities for Quadratic Programming with Continuous Variables and Binary Indicators

- MathematicsIPCO
- 2013

It is shown that adding the perspective constraints to a semidefinite programming relaxation of convex quadratic programs with binary indicators results in a problem whose bound is equivalent to the recent optimal diagonal splitting approach of Zheng et al.

### Effective separation of disjunctive cuts for convex mixed integer nonlinear programs

- Mathematics
- 2010

We describe a computationally effective method for generating disjunctive inequalities for convex mixed-integer nonlinear programs (MINLPs). The method relies on solving a sequence of cut-generating…

### Lift-and-Project Cuts for Mixed Integer Convex Programs

- Computer ScienceIPCO
- 2011

A new method for strengthening the continuous relaxations of mixed integer nonlinear programs where the objective is linear and the relations between the decision variables are described by convex functions defining a convex feasible region is proposed.

### Strong-branching inequalities for convex mixed integer nonlinear programs

- MathematicsComput. Optim. Appl.
- 2014

Computational results reveal that existing algorithms can be significantly improved by leveraging the information generated as a byproduct of strong branching in the form of valid inequalities.

### Valid Linear Inequalities for Fixed Charge Problems

- MathematicsOper. Res.
- 1985

Two classes of facet-defining linear inequalities of the convex hull of X are derived, and it is shown that the second of these classes gives a complete description of the conveyance when mj = m for all j, and methods to detect violated inequalities are developed.

### Sequence Independent Lifting for Mixed-Integer Programming

- MathematicsOper. Res.
- 2004

It is seen that nonlinearity in lifting problems is resolved easily with superadditive lifting functions, which may pave the way for efficient applications of lifting with general integer variables.

### Perspective cuts for a class of convex 0–1 mixed integer programs

- EconomicsMath. Program.
- 2006

Using perspective cuts substantially improves the performance of Branch & Cut approaches for at least two models that have the required structure: the Unit Commitment problem in electrical power production and the Mean-Variance problem in portfolio optimization.

### Mixed-integer nonlinear optimization*†

- Computer Science, MathematicsActa Numerica
- 2013

An emerging area of mixed-integer optimal control that adds systems of ordinary differential equations to MINLP is described and a range of approaches for tackling this challenging class of problems are discussed, including piecewise linear approximations, generic strategies for obtaining convex relaxations for non-convex functions, spatial branch-and-bound methods, and a small sample of techniques that exploit particular types of non- Convex structures to obtain improved convex Relaxations.

### Algorithms and Software for Convex Mixed Integer Nonlinear Programs

- Computer Science
- 2012

This paper provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and…

### Valid inequalities for mixed 0-1 programs

- MathematicsDiscret. Appl. Math.
- 1986