Derivative free algorithms for nonsmooth and global optimization with application in cluster analysis
- Authors: Ganjehlou, Asef Nazari
- Date: 2009
- Type: Text , Thesis , PhD
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- Description: This thesis is devoted to the development of algorithms for solving nonsmooth nonconvex problems. Some of these algorithms are derivative free methods.
- Description: Doctor of Philosophy
G-coupling functions and properties of strongly star-shaped cones
- Authors: Morales-Silva, Daniel
- Date: 2009
- Type: Text , Thesis , PhD
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- Description: The main part of this thesis presents a new approach to the topic of conjugation, with applications to various optimization problems. It does so by introducing (what we call) G-coupling functions.
- Description: Doctor of Philosophy
Conditions for global minimum through abstract convexity
- Authors: Sharikov, Evgenii
- Date: 2008
- Type: Text , Thesis , PhD
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- Description: The theory of abstract convexity generalizes ideas of convex analysis by using the notion of global supports and the global definition of subdifferential. In order to apply this theory to optimization, we need to extend subdifferential calculus and separation properties into the area of abstract convexity.
- Description: Doctor of Philosophy
Application of nonsmooth optimisation to data analysis
- Authors: Ugon, Julien
- Date: 2005
- Type: Text , Thesis , PhD
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- Description: The research presented in this thesis is two-fold: on the one hand, major data mining problems are reformulated as mathematical programming problems. These problems should be carefully designed, since from their formulation depends the efficiency, perhaps the existence, of the solvers. On the other hand, optimisation methods are adapted to solve these problems, most of which are nonsmooth and nonconvex. This part is delicate, as the solution is often required to be good and obtained fast. Numerical experiments on real-world datasets are presented and analysed.
- Description: Doctor of Philosophy
Derivative-free hybrid methods in global optimization and their applications
- Authors: Zhang, Jiapu
- Date: 2005
- Type: Text , Thesis , PhD
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- Description: In recent years large-scale global optimization (GO) problems have drawn considerable attention. These problems have many applications, in particular in data mining and biochemistry. Numerical methods for GO are often very time consuming and could not be applied for high-dimensional non-convex and / or non-smooth optimization problems. The thesis explores reasons why we need to develop and study new algorithms for solving large-scale GO problems .... The thesis presents several derivative-free hybrid methods for large scale GO problems. These methods do not guarantee the calculation of a global solution; however, results of numerical experiments presented in this thesis demonstrate that they, as a rule, calculate a solution which is a global one or close to it. Their applications to data mining problems and the protein folding problem are demonstrated.
- Description: Doctor of Philosophy