Newton's Method for Multiobjective Optimization
From MaRDI portal
Publication:3563897
DOI10.1137/08071692XzbMath1195.90078OpenAlexW2004586020MaRDI QIDQ3563897
Jörg Fliege, L. M. Graña Drummond, Benar Fux Svaiter
Publication date: 1 June 2010
Published in: SIAM Journal on Optimization (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/08071692x
multiobjective programmingscalarizationoptimality conditionmulticriteria optimizationquadratic approximationPareto pointsNewtons method
Numerical mathematical programming methods (65K05) Multi-objective and goal programming (90C29) Nonlinear programming (90C30) Numerical methods based on nonlinear programming (49M37) Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) (49J30)
Related Items
An incremental descent method for multi-objective optimization ⋮ Geometric Duality Results and Approximation Algorithms for Convex Vector Optimization Problems ⋮ Variable metric method for unconstrained multiobjective optimization problems ⋮ Augmented Lagrangian cone method for multiobjective optimization problems with an application to an optimal control problem ⋮ An accelerated proximal gradient method for multiobjective optimization ⋮ Spectral conjugate gradient methods for vector optimization problems ⋮ Quasi-Newton algorithms for solving interval-valued multiobjective optimization problems by using their certain equivalence ⋮ Multiobjective optimization with least constraint violation: optimality conditions and exact penalization ⋮ Newton’s method for uncertain multiobjective optimization problems under finite uncertainty sets ⋮ Complexity bound of trust-region methods for convex smooth unconstrained multiobjective optimization ⋮ Improved front steepest descent for multi-objective optimization ⋮ Convergence rates of the stochastic alternating algorithm for bi-objective optimization ⋮ Convergence of inexact steepest descent algorithm for multiobjective optimizations on Riemannian manifolds without curvature constraints ⋮ A new scheme for approximating the weakly efficient solution set of vector rational optimization problems ⋮ Pareto front approximation through a multi-objective augmented Lagrangian method ⋮ Twenty years of continuous multiobjective optimization in the twenty-first century ⋮ Conditional gradient method for vector optimization ⋮ An adaptive consensus based method for multi-objective optimization with uniform Pareto front approximation ⋮ Multiobjective BFGS method for optimization on Riemannian manifolds ⋮ An infeasible interior-point technique to generate the nondominated set for multiobjective optimization problems ⋮ Multiobjective conjugate gradient methods on Riemannian manifolds ⋮ A Barzilai-Borwein descent method for multiobjective optimization problems ⋮ A Newton-type proximal gradient method for nonlinear multi-objective optimization problems ⋮ A memetic procedure for global multi-objective optimization ⋮ A trust-region approach for computing Pareto fronts in multiobjective optimization ⋮ Newton's method for interval-valued multiobjective optimization problem ⋮ Density function-based trust region algorithm for approximating Pareto front of black-box multiobjective optimization problems ⋮ MONOTONICITY FOR MULTIOBJECTIVE ACCELERATED PROXIMAL GRADIENT METHODS ⋮ Unnamed Item ⋮ Derivative-Free Feasible Backtracking Search Methods for Nonlinear Multiobjective Optimization with Simple Boundary Constraint ⋮ Extended Newton Methods for Multiobjective Optimization: Majorizing Function Technique and Convergence Analysis ⋮ A Newton method for capturing Pareto optimal solutions of fuzzy multiobjective optimization problems ⋮ A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization ⋮ Proximal point algorithm for differentiable quasi-convex multiobjective optimization ⋮ A proximal gradient splitting method for solving convex vector optimization problems ⋮ On high-order model regularization for multiobjective optimization ⋮ Charnes-Cooper scalarization and convex vector optimization ⋮ DTSMA: dominant swarm with adaptive T-distribution mutation-based slime mould algorithm ⋮ Multiple reduced gradient method for multiobjective optimization problems ⋮ Reduced Jacobian method ⋮ On \(q\)-steepest descent method for unconstrained multiobjective optimization problems ⋮ An external penalty-type method for multicriteria ⋮ On inexact projected gradient methods for solving variable vector optimization problems ⋮ Expensive multi-objective optimization of electromagnetic mixing in a liquid metal ⋮ A steepest descent-like method for vector optimization problems with variable domination structure ⋮ A nonmonotone gradient method for constrained multiobjective optimization problems ⋮ Barzilai and Borwein's method for multiobjective optimization problems ⋮ A study of Liu-Storey conjugate gradient methods for vector optimization ⋮ A modified Quasi-Newton method for vector optimization problem ⋮ Inexact projected gradient method for vector optimization ⋮ Newton-like methods for efficient solutions in vector optimization ⋮ A Newton-like method for variable order vector optimization problems ⋮ Inertial forward–backward methods for solving vector optimization problems ⋮ Trust region globalization strategy for the nonconvex unconstrained multiobjective optimization problem ⋮ An inexact restoration approach to optimization problems with multiobjective constraints under weighted-sum scalarization ⋮ Using first-order information in direct multisearch for multiobjective optimization ⋮ A penalty decomposition approach for multi-objective cardinality-constrained optimization problems ⋮ A sequential quadratically constrained quadratic programming technique for a multi-objective optimization problem ⋮ Quadratic scalarization for decomposed multiobjective optimization ⋮ A conjugate directions-type procedure for quadratic multiobjective optimization ⋮ A quasi-Newton method with Wolfe line searches for multiobjective optimization ⋮ Multi agent collaborative search based on Tchebycheff decomposition ⋮ An efficient hybrid algorithm for multiobjective optimization problems with upper and lower bounds in engineering ⋮ An inexact steepest descent method for multicriteria optimization on Riemannian manifolds ⋮ A subgradient method for multiobjective optimization on Riemannian manifolds ⋮ An adaptive nonmonotone line search for multiobjective optimization problems ⋮ Strong and weak conditions of regularity and optimality ⋮ The multiobjective steepest descent direction is not Lipschitz continuous, but is Hölder continuous ⋮ Proximal gradient methods for multiobjective optimization and their applications ⋮ A trust region method for solving multicriteria optimization problems on Riemannian manifolds ⋮ Quasi-Newton methods for solving multiobjective optimization ⋮ On the extension of the Hager-Zhang conjugate gradient method for vector optimization ⋮ Multi Agent Collaborative Search ⋮ Nonmonotone gradient methods for vector optimization with a portfolio optimization application ⋮ Convergence rates analysis of a multiobjective proximal gradient method ⋮ An interior proximal method in vector optimization ⋮ Memory gradient method for multiobjective optimization ⋮ A limited memory quasi-Newton approach for multi-objective optimization ⋮ Unnamed Item ⋮ The Gradient Subspace Approximation and Its Application to Bi-objective Optimization Problems ⋮ A cutting-plane method to nonsmooth multiobjective optimization problems ⋮ A novel hybrid algorithm for solving multiobjective optimization problems with engineering applications ⋮ A steepest descent-like method for variable order vector optimization problems ⋮ Quasi-Newton methods for multiobjective optimization problems ⋮ Multicriteria optimization with a multiobjective golden section line search ⋮ A Trust-Region Algorithm for Heterogeneous Multiobjective Optimization ⋮ A Globally Convergent SQCQP Method for Multiobjective Optimization Problems ⋮ The Proximal Point Method for Locally Lipschitz Functions in Multiobjective Optimization with Application to the Compromise Problem ⋮ Multiple subgradient descent bundle method for convex nonsmooth multiobjective optimization ⋮ A barrier-type method for multiobjective optimization ⋮ A weighting subgradient algorithm for multiobjective optimization ⋮ Extension of Zoutendijk method for solving constrained multiobjective optimization problems ⋮ A relaxed projection method for solving multiobjective optimization problems ⋮ A new reduced gradient method for solving linearly constrained multiobjective optimization problems ⋮ Quasi-Newton's method for multiobjective optimization ⋮ A quadratically convergent Newton method for vector optimization ⋮ The self regulation problem as an inexact steepest descent method for multicriteria optimization ⋮ Nonsmooth multiobjective programming with quasi-Newton methods ⋮ Unconstrained steepest descent method for multicriteria optimization on Riemannian manifolds ⋮ Newton’s method for variational inequality problems: Smale’s point estimate theory under the γ-condition ⋮ Hypervolume Maximization via Set Based Newton’s Method ⋮ A New Predictor Corrector Variant for Unconstrained Bi-objective Optimization Problems ⋮ Convergence of the projected gradient method for quasiconvex multiobjective optimization ⋮ Nonmonotone line searches for unconstrained multiobjective optimization problems ⋮ Constraint qualifications for Karush-Kuhn-Tucker conditions in multiobjective optimization ⋮ Accelerated diagonal steepest descent method for unconstrained multiobjective optimization ⋮ Conditional gradient method for multiobjective optimization ⋮ Nonlinear Conjugate Gradient Methods for Vector Optimization ⋮ Complexity of gradient descent for multiobjective optimization ⋮ An efficient descent method for locally Lipschitz multiobjective optimization problems ⋮ Robust multiobjective optimization \& applications in portfolio optimization ⋮ A proximal point-type method for multicriteria optimization ⋮ A strongly convergent proximal point method for vector optimization ⋮ A research survey: review of flexible job shop scheduling techniques ⋮ A proximal point method for difference of convex functions in multi-objective optimization with application to group dynamic problems ⋮ Tracing Locally Pareto-Optimal Points by Numerical Integration ⋮ Convergence of a nonmonotone projected gradient method for nonconvex multiobjective optimization ⋮ On \(q\)-Newton's method for unconstrained multiobjective optimization problems ⋮ Iteration-complexity and asymptotic analysis of steepest descent method for multiobjective optimization on Riemannian manifolds ⋮ A sequential quadratic programming method for constrained multi-objective optimization problems ⋮ A Method for Constrained Multiobjective Optimization Based on SQP Techniques ⋮ Multi-criteria optimization in regression ⋮ On the convergence of the projected gradient method for vector optimization ⋮ A new scalarization and numerical method for constructing the weak Pareto front of multi-objective optimization problems ⋮ Globally convergent Newton-type methods for multiobjective optimization ⋮ On the convergence of steepest descent methods for multiobjective optimization ⋮ An augmented Lagrangian algorithm for multi-objective optimization ⋮ Adaptive trust region scheme for multi-objective optimization problem using Geršgorin circle theorem ⋮ Combined gradient methods for multiobjective optimization ⋮ Trust region methods for solving multiobjective optimisation ⋮ Steepest descent methods for critical points in vector optimization problems ⋮ Newton-like methods for solving vector optimization problems ⋮ Linear convergence of a nonmonotone projected gradient method for multiobjective optimization ⋮ Nonmonotone trust region algorithm for solving the unconstrained multiobjective optimization problems