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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... (Update)
Context of citations to this paper: More
...expressions with the addition of separable quadratic functions, which aim to overpower the nonconvexities. In Adjiman and Floudas [1] convex lower bound functions for general twice differentiable functions are based on second order information. Using so called interval...
.... global optimisation problems and nonlinear systems which are de ned by arbitrary arithmetical expressions, see Adjiman and Floudas [1] and Androulakis, Maranas, and Floudas [3] There convex lower bound functions are constructed by augmenting the nonconvex expressions...
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BibTeX entry: (Update)
C. S. Adjiman and C. A. Floudas, Rigorous convex underestimators for general twice--differentiable problems, J. Glob. Opt. 9 (1996), 23--40. http://citeseer.ist.psu.edu/146850.html More
@misc{ adjiman96rigorous,
author = "C. Adjiman and C. Floudas",
title = "Rigorous convex underestimators for general twice--differentiable problems",
text = "C. S. Adjiman and C. A. Floudas, Rigorous convex underestimators for general
twice--differentiable problems, J. Glob. Opt. 9 (1996), 23--40.",
year = "1996",
url = "citeseer.ist.psu.edu/146850.html" }
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35 Handbook for Automatic Computation (context) - Reinsch, Wilkinson et al. - 1971
34 A Primal-Relaxed Dual Global Optimization Approach - Floudas, Visweswaran - 1993
33 Towards Global Optimization (context) - Dixon, Szego - 1990
31 Jointly Constrained Biconvex Programming (context) - Al-Khayyal, Falk - 1983
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22 Asymptotic Stability of an Equilibrium Position of a Family .. (context) - Kharitonov - 1979
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4 fraser publishing company (context) - Brooke, Kendrick et al. - 1992
1 the Eigenvalues of Interval Matrices (context) - Hollot, Bartlett - 1987
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