A cell exclusion algorithm for determining all the solutions of a nonlinear system of equations
Applied Mathematics and Computation
Piecewise Linear Modeling and Analysis
Piecewise Linear Modeling and Analysis
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Finding all solutions of nonlinear equations using the dual simplex method
Journal of Computational and Applied Mathematics - Proceedings of the international conference on recent advances in computational mathematics
Efficient and Safe Global Constraints for Handling Numerical Constraint Systems
SIAM Journal on Numerical Analysis
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Algorithm 852: RealPaver: an interval solver using constraint satisfaction techniques
ACM Transactions on Mathematical Software (TOMS)
Approximating separable nonlinear functions via mixed zero-one programs
Operations Research Letters
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Finding all solutions of nonlinear or piecewise-linear equations is an important problem which is widely encountered in science and engineering. Various algorithms have been proposed for this problem. However, the implementation of these algorithms are generally difficult for non-experts or beginners. In this paper, an efficient method is proposed for finding all solutions of separable systems of piecewise-linear equations using integer programming. In this method, we formulate the problem of finding all solutions by a mixed integer programming problem, and solve it by a high-performance integer programming software such as GLPK, SCIP, or CPLEX. It is shown that the proposed method can be easily implemented without making complicated programs. It is also confirmed by numerical examples that the proposed method can find all solutions of medium-scale systems of piecewise-linear equations in practical computation time.