Theory of functional connections applied to quadratic and nonlinear programming under equality constraints

This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fu...

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Bibliographic Details
Published in:arXiv.org
Main Authors: Mai, Tina, Mortari, Daniele
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 25.08.2022
Subjects:
Constraints
Equality
Iterative methods
Lagrange multiplier
Mathematical analysis
Mathematical programming
Newton methods
Nonlinear programming
Optimization
Quadratic programming
ISSN:2331-8422
Online Access:Get full text
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Summary:This paper introduces an efficient approach to solve quadratic and nonlinear programming problems subject to linear equality constraints via the Theory of Functional Connections. This is done without using the traditional Lagrange multiplier technique. More specifically, two distinct expressions (fully satisfying the equality constraints) are provided, to first solve the constrained quadratic programming problem as an unconstrained one for closed-form solution. Such expressions are derived via using an optimization variable vector, which is called the free vector \(\boldsymbol{g}\) by the Theory of Functional Connections. In the spirit of this Theory, for the equality constrained nonlinear programming problem, its solution is obtained by the Newton's method combining with elimination scheme in optimization. Convergence analysis is supported by a numerical example for the proposed approach.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1910.04917