320 research outputs found
Canonical duality for solving general nonconvex constrained problems
This paper presents a canonical duality theory for solving a general nonconvex constrained optimization problem within a unified framework to cover Lagrange multiplier method and KKT theory. It is proved that if both target function and constraints possess certain patterns necessary for modeling real systems, a perfect dual problem (without duality gap) can be obtained in a unified form with global optimality conditions provided.While the popular augmented Lagrangian method may produce more difficult nonconvex problems due to the nonlinearity of constraints. Some fundamental concepts such as the objectivity and Lagrangian in nonlinear programming are addressed
Neural networks, surrogate models and black box algorithms: theory and applications
In this Ph. D. Thesis we will analyze some of the most used surrogate models,
together with a particular type of line search black box strategy. After introducing
these powerful tools, we will present the Canonical Duality Theory, the potentiality
it has to improve these tools, and some of their applications.
The principal contributes of this Thesis are the reformulation of the Radial Basis
Neural Network problem in its canonical dual form in Section 2.2 and the application
of the surrogate models and black box algorithms presented in this Thesis on various
real world problems reported in Chapter 3
Neural networks, surrogate models and black box algorithms: theory and applications
In this Ph. D. Thesis we will analyze some of the most used surrogate models,
together with a particular type of line search black box strategy. After introducing
these powerful tools, we will present the Canonical Duality Theory, the potentiality
it has to improve these tools, and some of their applications.
The principal contributes of this Thesis are the reformulation of the Radial Basis
Neural Network problem in its canonical dual form in Section 2.2 and the application
of the surrogate models and black box algorithms presented in this Thesis on various
real world problems reported in Chapter 3
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