Theory of functional connections applied to nonlinear programming under equality constraints

10/11/2019
by   Tina Mai, et al.
0

This paper introduces an efficient approach to solve quadratic programming problems subject to equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multipliers approach, and the solution is provided in closed-form. Two distinct constrained expressions (satisfying the equality constraints) are introduced. The unknown vector optimization variable is then the free vector g, introduced by the Theory of Functional Connections, to derive constrained expressions. The solution to the general nonlinear programming problem is obtained by the Newton's method in optimization, and each iteration involves the second-order Taylor approximation, starting from an initial vector x^(0) which is a solution of the equality constraint. To solve the quadratic programming problems, we not only introduce the new approach but also provide a numerical accuracy and speed comparisons with respect to MATLAB's . To handle the nonlinear programming problem using the Theory of Functional Connections, convergence analysis of the proposed approach is provided.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/10/2020

Least-squares Solutions of Eighth-order Boundary Value Problems using the Theory of Functional Connections

This paper shows how to obtain highly accurate solutions of eighth-order...
research
06/20/2022

Sample Average Approximation for Stochastic Programming with Equality Constraints

We revisit the sample average approximation (SAA) approach for general n...
research
08/19/2016

Critical Points for Two-view Triangulation

Two-view triangulation is a problem of minimizing a quadratic polynomial...
research
06/29/2020

A Nonmonotone Matrix-Free Algorithm for Nonlinear Equality-Constrained Inverse Problems

Least squares form one of the most prominent classes of optimization pro...
research
01/08/2021

Nonlinear Optimization in R using nlopt

In this article, we present a problem of nonlinear constraint optimizati...
research
07/28/2020

Bijective Mapping Analysis to Extend the Theory of Functional Connections to Non-rectangular 2-dimensional Domains

This work presents an initial analysis of using bijective mappings to ex...
research
11/09/2022

Nonlinear Set Membership Filter with State Estimation Constraints via Consensus-ADMM

This paper considers the state estimation problem for nonlinear dynamic ...

Please sign up or login with your details

Forgot password? Click here to reset