Newton-like methods for efficient solutions in vector optimization
Computational Optimization and Applications
Inexact projected gradient method for vector optimization
Computational Optimization and Applications
Comprehensive Survey of the Hybrid Evolutionary Algorithms
International Journal of Applied Evolutionary Computation
Multi Agent Collaborative Search based on Tchebycheff decomposition
Computational Optimization and Applications
Quasi-Newton's method for multiobjective optimization
Journal of Computational and Applied Mathematics
An Optimization Rule for In Silico Identification of Targeted Overproduction in Metabolic Pathways
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We propose an extension of Newton's method for unconstrained multiobjective optimization (multicriteria optimization). This method does not use a priori chosen weighting factors or any other form of a priori ranking or ordering information for the different objective functions. Newton's direction at each iterate is obtained by minimizing the max-ordering scalarization of the variations on the quadratic approximations of the objective functions. The objective functions are assumed to be twice continuously differentiable and locally strongly convex. Under these hypotheses, the method, as in the classical case, is locally superlinear convergent to optimal points. Again as in the scalar case, if the second derivatives are Lipschitz continuous, the rate of convergence is quadratic. Our convergence analysis uses a Kantorovich-like technique. As a byproduct, existence of optima is obtained under semilocal assumptions.