New Newton Group Iterative Methods for Solving Large-Scale Multi-Objective Constrained Optimization Problems (European Journal of Pure and Applied Mathematics, 2025)
With the rapid development of big data and artificial intelligence technologies, we are facing increasingly complex data and decision-making problems. Solving large-scale multi-objective constrained optimization problems can help to solve many practical engineering and scientific problems. The weighted and Lagrange multiplier methods are considered to be classical and effective methods for dealing with multiple objectives and constraints, but there are some difficulties in solving the processed unconstrained optimization problems.The Newton method is a commonly used method for solving this type of problem, but it requires a high computational complexity. In order to solve these difficulties, we combine four methods such as the Weighted method, Lagrange multiplier method, Newton's method and Explicit Group Gauss-Seidel iterative method to propose new Newton Group iterative methods such as 2 and 4-point Explicit Group Gauss-Seidel iterative methods namely as Newton-2EGGS and Newton-4EGGS for solving large-scale multi-objective constrained optimization problems. Also, the convergence analysis of the proposed method is presented. To test the superiority of the proposed method by comparing the computational results, the Newton-4EGGS iteration is more efficient than both Newton-2EGGS iterative method and the Newton-Gauss-Seidel iterative method (Newton-GS), especially in terms of the number of iterations and the computational time.
Keywords: multi-objective constrained optimization, weighted method, Lagrange multiplier method, Newton method, Explicit Group iterative method