Nonlinear programming: theory, algorithms, and applications
Nonlinear programming: theory, algorithms, and applications
Interval analysis: theory and applications
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Analysis of Bounds for Multilinear Functions
Journal of Global Optimization
Convexification and Global Optimization in Continuous And
Convexification and Global Optimization in Continuous And
Global optimization of mixed-integer nonlinear programs: A theoretical and computational study
Mathematical Programming: Series A and B
Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems
Journal of Global Optimization
Journal of Global Optimization
Interval methods for semi-infinite programs
Computational Optimization and Applications
A polyhedral branch-and-cut approach to global optimization
Mathematical Programming: Series A and B
Global solution of semi-infinite programs
Mathematical Programming: Series A and B
On the Liu---Floudas Convexification of Smooth Programs
Journal of Global Optimization
Methods and Applications of Interval Analysis (SIAM Studies in Applied and Numerical Mathematics) (Siam Studies in Applied Mathematics, 2.)
Journal of Global Optimization
Tight convex underestimators for $${{\mathcal C}^2}$$-continuous problems: I. univariate functions
Journal of Global Optimization
Relaxation-Based Bounds for Semi-Infinite Programs
SIAM Journal on Optimization
Branching and bounds tighteningtechniques for non-convex MINLP
Optimization Methods & Software - GLOBAL OPTIMIZATION
McCormick-Based Relaxations of Algorithms
SIAM Journal on Optimization
The theoretical and empirical rate of convergence for geometric branch-and-bound methods
Journal of Global Optimization
Convergence analysis of Taylor models and McCormick-Taylor models
Journal of Global Optimization
Improved relaxations for the parametric solutions of ODEs using differential inequalities
Journal of Global Optimization
Journal of Global Optimization
Hi-index | 0.00 |
Theory for the convergence order of the convex relaxations by McCormick (Math Program 10(1):147---175, 1976) for factorable functions is developed. Convergence rules are established for the addition, multiplication and composition operations. The convergence order is considered both in terms of pointwise convergence and of convergence in the Hausdorff metric. The convergence order of the composite function depends on the convergence order of the relaxations of the factors. No improvement in the order of convergence compared to that of the underlying bound calculation, e.g., via interval extensions, can be guaranteed unless the relaxations of the factors have pointwise convergence of high order. The McCormick relaxations are compared with the 驴BB relaxations by Floudas and coworkers (J Chem Phys, 1992, J Glob Optim, 1995, 1996), which guarantee quadratic convergence. Illustrative and numerical examples are given.