# Three ideas for a feasibility pump for nonconvex MINLP

@article{Belotti2017ThreeIF, title={Three ideas for a feasibility pump for nonconvex MINLP}, author={Pietro Belotti and Timo Berthold}, journal={Optimization Letters}, year={2017}, volume={11}, pages={3-15} }

We describe an implementation of the Feasibility Pump heuristic for nonconvex MINLPs. Our implementation takes advantage of three novel techniques, which we discuss here: a hierarchy of procedures for obtaining an integer solution, a generalized definition of the distance function that takes into account the nonlinear character of the problem, and the insertion of linearization cuts for nonconvex constraints at every iteration. We implemented this new variant of the Feasibility Pump as part of…

## 5 Citations

### Polyhedral Approximation Strategies in Nonconvex Mixed-Integer Nonlinear Programming*

- Computer Science
- 2020

Some extensions to SHOT are discussed that significantly extend its applicability to nonconvex problems, including utilizing convexity detection for selecting the nonlinearities to linearize, lifting reformulations for special classes of functions, feasibility relaxations for infeasible subproblems and adding objective cuts to force the search for better feasible solutions.

### Polyhedral approximation strategies for nonconvex mixed-integer nonlinear programming in SHOT

- Computer ScienceJ. Glob. Optim.
- 2022

Some extensions to SHOT are discussed that significantly extend its applicability to nonconvex problems, including utilizing convexity detection for selecting the nonlinearities to linearize, lifting reformulations for special classes of functions, feasibility relaxations for infeasible subproblems and adding objective cuts to force the search for better feasible solutions.

### Ten years of feasibility pump, and counting

- PsychologyEURO J. Comput. Optim.
- 2019

An overview of the diverse Feasibility Pump literature that has been presented over the last decade is provided.

### Feasibility Pump Algorithm for Sparse Representation under Laplacian Noise

- Computer ScienceMathematical Problems in Engineering
- 2019

The Feasibility Pump recovers the sparse representation of signals affected by Laplacian noise with good accuracy while using a very small computation time when compared with other mixed integer methods.

### Integrality gap minimization heuristics for binary mixed integer nonlinear programming

- Computer Science, BusinessJ. Glob. Optim.
- 2018

Two feasibility heuristics for binary mixed integer nonlinear programming are presented based on the solution of integrality gap minimization problems with a space partitioning scheme defined over the integer variables of the problem addressed.

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