Nonconvex multiobjective programming

New adaptive proximal gradient algorithms for solving multiobjective composite optimization problems

Categories Nonlinear Optimization, Nonsmooth Optimization, Robust Optimization Tags , , , ,

In this paper, we propose new adaptive proximal gradient algorithms to solve multiobjective optimization problems, where each objective function is the sum of a differentiable function and a proper, closed, convex function. Utilizing the local behavior of the differentiable terms we propose new adaptive ways to select stepsizes used in proximal gradient scheme. In particular, … Read more

Steepest descent method using novel adaptive stepsizes for unconstrained nonlinear multiobjective programming

Categories Convex Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

We propose new adaptive strategies to compute stepsizes for the steepest descent method to solve unconstrained nonlinear multiobjective optimization problems without employing any linesearch procedure. The resulting algorithms can be applied to a wide class of nonconvex unconstrained multi-criteria optimization problems satisfying a global Lipschitz continuity condition imposed on the gradients of all objectives. In … Read more