On the convergence of global methods in multiextremal optimization
Journal of Optimization Theory and Applications
Stochastic global optimization methods. part 1: clustering methods
Mathematical Programming: Series A and B
Stochastic global optimization methods. part 11: multi level methods
Mathematical Programming: Series A and B
Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Computational Experience with a New Class of Convex Underestimators: Box-constrained NLP Problems
Journal of Global Optimization
Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications)
A new global optimization method for univariate constrained twice-differentiable NLP problems
Journal of Global Optimization
Journal of Global Optimization
Tight convex underestimators for $${{\mathcal C}^2}$$-continuous problems: I. univariate functions
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Convex relaxation for solving posynomial programs
Journal of Global Optimization
Solutions to quadratic minimization problems with box and integer constraints
Journal of Global Optimization
An Efficient Global Approach for Posynomial Geometric Programming Problems
INFORMS Journal on Computing
Convergence rate of McCormick relaxations
Journal of Global Optimization
Convergence analysis of Taylor models and McCormick-Taylor models
Journal of Global Optimization
A reformulation framework for global optimization
Journal of Global Optimization
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We present a new class of convex underestimators for arbitrarily nonconvex and twice continuously differentiable functions. The underestimators are derived by augmenting the original nonconvex function by a nonlinear relaxation function. The relaxation function is a separable convex function, that involves the sum of univariate parametric exponential functions. An efficient procedure that finds the appropriate values for those parameters is developed. This procedure uses interval arithmetic extensively in order to verify whether the new underestimator is convex. For arbitrarily nonconvex functions it is shown that these convex underestimators are tighter than those generated by the 驴BB method. Computational studies complemented with geometrical interpretations demonstrate the potential benefits of the proposed improved convex underestimators.