(2) The convexification method for the collision avoidance constraints and the sequential convex programming
for solving the underlying optimization problem in MPC are effective.
The proposed method is based on minimizing a novel objective function in the form of a difference of convex programming
Therefore, the constrained quadratic programming problem (46) is a convex programming
problem, by Theorem 20.
The numerical implementation of the two proposed approaches takes advantage of the CVX Matlab[R] toolbox [44, 45], a general software for convex programming
A Bisection Method for Convex Programming
Problem Solution based on Projection Neural Network.
As we know, convex programming
is a special kind of non-linear programming.
Thus, one can convert (MP) into the following equivalent reverse convex programming
We emphasize the theories of Nesterov and Nemirovsky  which use this class of functions for developing linear and convex quadratic programs with convex quadratic constraints, and Udriste's works ,  which develop barrier methods for smooth convex programming
on Riemannian manifolds.
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
ADMM can be viewed as an application of the Douglas-Rachford splitting method to the dual of the two-block separable convex programming(2)  or a special case of the proximal point method for the general convex programming
, or a generalization of the classical Uzawa method for solving the saddle-point problems .
The concepts of the [phi]-convex and [phi]-invex functions have played very important role in the development of generalized convex programming
. From definitions 2.2 and 2.3, it is clear that the differentiable [phi]-convex function are [phi]-invex functions.
Fukushima, "Application of the alternating direction method of multipliers to separable convex programming
problems," Computational Optimization and Applications, vol.