An inexact steepest descent method for multicriteria optimization on Riemannian manifolds

DOI10.1007/s10957-013-0305-9zbMath1295.90067OpenAlexW2084127566WikidataQ115382574 ScholiaQ115382574MaRDI QIDQ382906

Glaydston C. Bento, Paulo Sérgio M. Santos, João Xavier da Cruz Neto

Publication date: 22 November 2013

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10957-013-0305-9

zbMATH Keywords

Riemannian manifoldsPareto optimalitysteepest descentquasi-convexitymulticriteria optimizationquasi-Fejér convergence

Mathematics Subject Classification ID

Multi-objective and goal programming (90C29) Programming in abstract spaces (90C48)

Related Items (12)

Proximal point methods for Lipschitz functions on Hadamard manifolds: scalar and vectorial cases ⋮ Reduced Jacobian method ⋮ Proximal point method for vector optimization on Hadamard manifolds ⋮ A trust region method for solving multicriteria optimization problems on Riemannian manifolds ⋮ A Benchmark Study on Steepest Descent and Conjugate Gradient Methods-Line Search Conditions Combinations in Unconstrained Optimization ⋮ Semivectorial bilevel optimization on Riemannian manifolds ⋮ Convergence of inexact steepest descent algorithm for multiobjective optimizations on Riemannian manifolds without curvature constraints ⋮ Inexact proximal point algorithm for quasiconvex optimization problems on Hadamard manifolds ⋮ Multiobjective BFGS method for optimization on Riemannian manifolds ⋮ Multiobjective conjugate gradient methods on Riemannian manifolds ⋮ Inexact proximal point methods for multiobjective quasiconvex minimization on Hadamard manifolds ⋮ Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds

Cites Work

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• Subgradient method for convex feasibility on Riemannian manifolds
• Convergence of the projected gradient method for quasiconvex multiobjective optimization
• Hybrid approximate proximal method with auxiliary variational inequality for vector optimization
• Monotone and accretive vector fields on Riemannian manifolds
• Local convergence of the proximal point method for a special class of nonconvex functions on Hadamard manifolds
• Smooth nonlinear optimization of \(\mathbb R^n\)
• Quasiconvex optimization and location theory
• Steepest descent methods for multicriteria optimization.
• Unconstrained steepest descent method for multicriteria optimization on Riemannian manifolds
• A steepest descent method for vector optimization
• A projected gradient method for vector optimization problems
• Inexact projected gradient method for vector optimization
• On the choice of parameters for the weighting method in vector optimization
• Steepest descent method with a generalized Armijo search for quasiconvex functions on Riemannian manifolds
• Sectional curvatures in nonlinear optimization
• Convex- and monotone-transformable mathematical programming problems and a proximal-like point method
• Vector Optimization
• On the convergence of the projected gradient method for vector optimization
• Newton's Method for Multiobjective Optimization
• Locally Geodesically Quasiconvex Functions on Complete Riemannian Manifolds
• Proximal Methods in Vector Optimization

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