A Gauss-Newton approach to solving generalized inequalities
Mathematics of Operations Research
New computer methods for global optimization
New computer methods for global optimization
The enclosure of solutions of parameter-dependent systems of equations
Reliability in computing: the role of interval methods in scientific computing
An interval algorithm for constrained global optimization
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Solving Polynomial Systems Using a Branch and Prune Approach
SIAM Journal on Numerical Analysis
On proving existence of feasible points in equality constrained optimization problems
Mathematical Programming: Series A and B
A Trust-Region Approach to Nonlinear Systems of Equalities and Inequalities
SIAM Journal on Optimization
Heuristic search and pruning in polynomial constraints satisfaction
Annals of Mathematics and Artificial Intelligence
Multisection in Interval Branch-and-Bound Methods for Global Optimization – I. Theoretical Results
Journal of Global Optimization
A hybrid global optimization method: the one-dimensional case
Journal of Computational and Applied Mathematics
Technical Communique: Interval constraint propagation with application to bounded-error estimation
Automatica (Journal of IFAC)
A hybrid global optimization method: the multi-dimensional case
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
Finding feasible points is important in optimization. There are currently two major classes of algorithms to deal with the problem of feasible points. The first class of algorithms (of local nature) is to find an approximate feasible point. Given a neighbourhood of an approximate feasible point, the second class of algorithms is to prove whether a feasible point exists inside this neighbourhood. To the best of our knowledge, no methods have been practically implemented to efficiently find the smallest boxes for bounding the feasible points defined by a system of nonlinear and nonconvex inequalities, unless the feasible set is convex. In this paper, we will present a numerical method to find the smallest boxes for bounding the feasible point sets defined by a nonlinear and nonconvex inequality and/or a system of nonlinear and nonconvex inequalities. Two examples have been synthetically constructed and used to show that the proposed numerical method can indeed correctly find all the smallest bounding boxes at any given accuracy efficiently. A brief comparison with relevant techniques will be discussed. Our method may also be thought of as the first solid theoretical basis for multisection and multisplitting in global optimization, when compared with those empirical ones in the literature.