A Stable and Efficient Method for Solving a Convex Quadratic Program with Application to Optimal Control

2012 ◽  
Vol 22 (4) ◽  
pp. 1369-1393 ◽  
Author(s):  
Amir Shahzad ◽  
Eric C. Kerrigan ◽  
George A. Constantinides
Keyword(s):  
Optimal Control ◽  
Efficient Method ◽  
Quadratic Program ◽  
Convex Quadratic Program

Optimal control of large nonlinear models: An efficient method of policy search applied to the Dutch economy

1983 ◽  
Vol 5 (2) ◽  
pp. 253-270 ◽  
Author(s):  
Andries S. Brandsma ◽  
A.J. Hughes Hallett ◽  
Nico van der Windt
Keyword(s):  
Optimal Control ◽  
Efficient Method ◽  
Nonlinear Models ◽  
Policy Search

scholarly journals Inverse KKT: Learning cost functions of manipulation tasks from demonstrations

2017 ◽  
Vol 36 (13-14) ◽  
pp. 1474-1488 ◽  
Author(s):  
Peter Englert ◽  
Ngo Anh Vien ◽  
Marc Toussaint
Keyword(s):  
Optimal Control ◽  
Cost Function ◽  
Hilbert Spaces ◽  
Reproducing Kernel ◽  
Cost Functions ◽  
Quadratic Program ◽  
Relevant Task ◽  
Kernel Hilbert Spaces ◽  
The Cost ◽  
Linear Parameterization

Inverse optimal control (IOC) assumes that demonstrations are the solution to an optimal control problem with unknown underlying costs, and extracts parameters of these underlying costs. We propose the framework of inverse Karush–Kuhn–Tucker (KKT), which assumes that the demonstrations fulfill the KKT conditions of an unknown underlying constrained optimization problem, and extracts parameters of this underlying problem. Using this we can exploit the latter to extract the relevant task spaces and parameters of a cost function for skills that involve contacts. For a typical linear parameterization of cost functions this reduces to a quadratic program, ensuring guaranteed and very efficient convergence, but we can deal also with arbitrary non-linear parameterizations of cost functions. We also present a non-parametric variant of inverse KKT that represents the cost function as a functional in reproducing kernel Hilbert spaces. The aim of our approach is to push learning from demonstration to more complex manipulation scenarios that include the interaction with objects and therefore the realization of contacts/constraints within the motion. We demonstrate the approach on manipulation tasks such as sliding a box, closing a drawer and opening a door.

Solving nonmonotone affine variational inequalities problem by DC programming and DCA

2018 ◽  
Vol 13 (03) ◽  
pp. 2050067
Author(s):  
Zahira Kebaili ◽  
Mohamed Achache
Keyword(s):  
Variational Inequalities ◽  
Numerical Experiments ◽  
Dc Programming ◽  
Quadratic Program ◽  
Test Problems ◽  
Speed Of Convergence ◽  
Difference Of Convex Functions ◽  
Convex Quadratic Program ◽  
Difference Of Convex

In this paper, we consider an optimization model for solving the nonmonotone affine variational inequalities problem (AVI). It is formulated as a DC (Difference of Convex functions) program for which DCA (DC Algorithms) are applied. The resulting DCA are simple: it consists of solving successive convex quadratic program. Numerical experiments on several test problems illustrate the efficiency of the proposed approach in terms of the quality of the obtained solutions and the speed of convergence.

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