He begins by setting out the theoretical foundations of optimality conditions, the

convex optimization problem, and Karuch-Kuhn-Tucher conditions and duality.

The test NDTPs, with quadratic cost function C, represents the

convex optimization problems, for which gradient-based MINLP techniques can find the global optimum solutions, provided that the solution time limit is large enough.

Recall some basic notions and definitions about

convex optimization.

k]) is a

convex optimization problem obtained from (P) under substitute the function h with its affine minorization defined by [y.

Convex optimization in signal processing and communications.

However, for a

convex optimization problem, all locally optimal solutions are globally optimal.

In nonlinear optimization problem,

convex optimization problem occupies a very important position because it has many good performances.

We show how recent advancements in

convex optimization for machine learning yields positive answers to some of the above questions: there exists cases in which much more efficient algorithms exist for learning practically important concepts.

VANDENBERGHE,

Convex Optimization, Cambridge University Press, Cambridge, 2004.

Stephen Boyd as a result of their research on the application of

convex optimization mathematics to analog circuit design.

of Dayton, Ohio) claim that large random matrices,

convex optimization, and game theory are analytical tools central to the next generation of cognitive radio networks.

SVMs reduce most machine learning problems to optimization problems, optimization lies at the heart of SVMs, especially the

convex optimization problem plays an important role in SVMs.