Journal of Multi Disciplinary Engineering Technologies
Volume 18 • Issue 02 • Published: May 2025 • ISSN (Print): 0974-1771 • ISSN (Online): 2581-9372
KKT Conditions for Variational Problem Involving Higher-Order Derivatives
Lokesh Kumar1, Sandeep Suman2, Shubhra3*
1 Department of Mathematics, S. M. College, TMBU, Bhagalpur, Bihar, 812001, India.
2 University Department of Mathematics, TMBU, Bhagalpur, Bihar, 812007, India.
3 Department of Mathematics, Patna University, Patna, Bihar, 800005, India.
*Corresponding author: drshubhrasuman@gmail.com
Contributing authors: lokeshkmath@gmail.com; drsandeepsuman@gmail.com
Abstract
In this article, we treat a generalization of the Lagrange problem of the calculus of variations by allowing the functional to depend on higher-order derivatives. We convert the problem to a mathematical programming formulation and derive the Karush–Kuhn–Tucker (KKT) necessary conditions. The resulting conditions generalize the classical Euler–Lagrange equations.
Keywords
KKT conditions
Variational problem
Mathematical programming
Convex optimization
Variational problem
Mathematical programming
Convex optimization
Article information
Journal: Journal of Multi Disciplinary Engineering Technologies
Volume / Issue: 18 / 02
Published: May 2025
ISSN (Print): 0974-1771
ISSN (Online): 2581-9372