Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems

Ramirez, V. A.; Sottosanto, Graciela N.

doi:10.1007/s10589-021-00346-8

Cited by 6 publications

(1 citation statement)

References 20 publications

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“…The area y here is no longer the original accepted area, the area is reduced, and the original point is deleted; so, it can be considered to be rejected by a. In Figure 3(d), the normal vector is pointing in the opposite direction, and the acceptable area is still reduced; so, it can be deleted [22]. The acceptable area intersects the acceptable area of the pyramid; so, the whole acceptable area is reduced to the enclosed area Y.…”

Section: Trust Region Algorithmmentioning

confidence: 99%

New Solutions of Nonlinear Equations Constrained by Bounded Variables under Edge Computation

Wang

2022

Wireless Communications and Mobile Computing

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Aiming at the problem of low global convergence and local convergence rate of trust region interior points of bounded variable constrained nonlinear equations, a trust region interior point algorithm for bounded variable constrained nonlinear equations under edge calculation is designed. By constructing the basic function form of nonlinear equations constrained by bounded variables, the boundary of nonlinear equations is determined by Gauss Newton iterative process to ensure the global convergence of changes; solve the original objective function, analyze the trust region subproblem of the unconstrained optimization problem, and generate an acceptable region. The region is generated through two-dimensional example interpretation. The interior points in the acceptable region are determined by the primal dual interior point method, and the interior points in the acceptable region are optimized. With the help of edge calculation, the trust region interior point programming model of bounded variable constrained nonlinear equations is designed to realize the algorithm design. The experimental results show that the designed algorithm can improve the trust region interior point global convergence and local convergence rate of nonlinear equations with bounded variable constraints.

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Section: Trust Region Algorithmmentioning

confidence: 99%

New Solutions of Nonlinear Equations Constrained by Bounded Variables under Edge Computation

Wang

2022

Wireless Communications and Mobile Computing

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Conditional gradient method for vector optimization

Chen¹,

Yang²,

Zhao³

2023

Comput Optim Appl

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A trust-region approach for computing Pareto fronts in multiobjective optimization

Mohammadi,

Custódio

2023

Comput Optim Appl

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Multiobjective optimization is a challenging scientific area, where the conflicting nature of the different objectives to be optimized changes the concept of problem solution, which is no longer a single point but a set of points, namely the Pareto front. In a posteriori preferences approach, when the decision maker is unable to rank objectives before the optimization, it is important to develop algorithms that generate approximations to the complete Pareto front of a multiobjective optimization problem, making clear the trade-offs between the different objectives. In this work, an algorithm based on a trust-region approach is proposed to approximate the set of Pareto critical points of a multiobjective optimization problem. Derivatives are assumed to be known, allowing the computation of Taylor models for the different objective function components, which will be minimized in two main steps: the extreme point step and the scalarization step. The goal of the extreme point step is to expand the approximation to the Pareto front, by moving towards the extreme points of it, corresponding to the individual minimization of each objective function component. The scalarization step attempts to reduce the gaps on the Pareto front, by solving adequate scalarization problems. The convergence of the method is analyzed and numerical experiments are reported, indicating the relevance of each feature included in the algorithmic structure and its competitiveness, by comparison against a state-of-art multiobjective optimization algorithm.

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Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems

Cited by 6 publications

References 20 publications

New Solutions of Nonlinear Equations Constrained by Bounded Variables under Edge Computation

New Solutions of Nonlinear Equations Constrained by Bounded Variables under Edge Computation

Conditional gradient method for vector optimization

A trust-region approach for computing Pareto fronts in multiobjective optimization

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