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convex programming

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convex programming

[′kän‚veks ′prō‚gram·iŋ]
(mathematics)
Nonlinear programming in which both the function to be maximized or minimized and the constraints are appropriately chosen convex or concave functions of the independent variables.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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References in periodicals archive
(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 (DCP) problem.
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 problem (RCP):
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.
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.
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.
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