Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration … Read more

A quasi-Newton method with Wolfe line searches for multiobjective optimization

We propose a BFGS method with Wolfe line searches for unconstrained multiobjective optimization problems. The algorithm is well defined even for general nonconvex problems. Global convergence and R-linear convergence to a Pareto optimal point are established for strongly convex problems. In the local convergence analysis, if the objective functions are locally strongly convex with Lipschitz … Read more

A study of Liu-Storey conjugate gradient methods for vector optimization

This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying … Read more

Globally convergent Newton-type methods for multiobjective optimization

We propose two Newton-type methods for solving (possibly) nonconvex unconstrained multiobjective optimization problems. The first is directly inspired by the Newton method designed to solve convex problems, whereas  the second uses  second-order information of the objective functions with ingredients of the steepest descent method.  One of the key points of our approaches  is to impose … Read more

Conditional gradient method for multiobjective optimization

We analyze the conditional gradient method, also known as Frank-Wolfe method, for constrained multiobjective optimization. The constraint set is assumed to be convex and compact, and the objectives functions are assumed to be continuously differentiable. The method is considered with different strategies for obtaining the step sizes. Asymptotic convergence properties and iteration-complexity bounds with and … Read more

On the extension of the Hager-Zhang conjugate gradient method for vector optimization

The extension of the Hager-Zhang (HZ) nonlinear conjugate gradient method for vector optimization is discussed in the present research. In the scalar minimization case, this method generates descent directions whenever, for example, the line search satisfies the standard Wolfe conditions. We first show that, in general, the direct extension of the HZ method for vector … Read more

A Wolfe line search algorithm for vector optimization

In a recent paper, Lucambio Pérez and Prudente extended the Wolfe conditions for the vector-valued optimization. Here, we propose a line search algorithm for finding a step-size satisfying the strong Wolfe conditions in the vector optimization setting. Well definiteness and finite termination results are provided. We discuss practical aspects related to the algorithm and present … Read more