## Rigorous Convex Underestimators for General Twice--Differentiable Problems (1996)

Venue: | Journal of Global Optimization |

Citations: | 35 - 15 self |

### BibTeX

@ARTICLE{Adjiman96rigorousconvex,

author = {Claire Adjiman and Christodoulos A. Floudas},

title = {Rigorous Convex Underestimators for General Twice--Differentiable Problems},

journal = {Journal of Global Optimization},

year = {1996},

volume = {9},

pages = {23--40}

}

### Years of Citing Articles

### OpenURL

### Abstract

. In order to generate valid convex lower bounding problems for nonconvex twice--differentiable optimization problems, a method that is based on second-- order information of general twice--differentiable functions is presented. Using interval Hessian matrices, valid lower bounds on the eigenvalues of such functions are obtained and used in constructing convex underestimators. By solving several nonlinear example problems, it is shown that the lower bounds are sufficiently tight to ensure satisfactory convergence of the ffBB, a branch and bound algorithm which relies on this underestimation procedure [3]. Key words: convex underestimators; twice--differentiable; interval anlysis; eigenvalues 1. Introduction The mathematical description of many physical phenomena, such as phase equilibrium, or of chemical processes generally requires the introduction of nonconvex functions. As the number of local solutions to a nonconvex optimization problem cannot be predicted a priori, the identifi...

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