The proposed method is based on minimizing a novel objective function in the form of a difference of convex programming (DCP) problem.

Activity Recognition via a Difference of Convex Programming Problem

A Bisection Method for

Convex Programming Problem Solution based on Projection Neural Network.

A mathematical programming is called convex programming if and only if its objective and constraint functions are convex.

As we know, convex programming is a special kind of non-linear programming.

As a consequence, by virtue of the choices which have been made in choosing the cost functional, one can assume that also the cost functional is a convex one, so that the overall problem is reduced to a

Convex Programming (CP) one.

We emphasize the theories of Nesterov and Nemirovsky [18] which use this class of functions for developing linear and convex quadratic programs with convex quadratic constraints, and Udriste's works [26], [28] which develop barrier methods for smooth convex programming on Riemannian manifolds.

Guler: Hyperbolic polynomials and interior point methods for convex programming, Math.

The efficient method for convex programming is multiple and it has perfect theory guarantees.

According to different closed convex constraint sets, we can pick and choose suitable convex programming algorithm to combine with our method.

In the case that the randomness of uncertain return rates follows normal distributions with deterministic covariance matrix, and the fuzziness is characterized by trapezoidal fuzzy variables, triangular fuzzy variables, or normal fuzzy variables, the proposed EV-ERV model is transformed into its deterministic convex programming models, which can be solved by general purpose optimization software.

Section 4 deals with the equivalent deterministic convex programming models under three situations.