Projected quasi-subgradient method for Hölder continuous quasi-convex multiobjective optimization

Abstract

We propose a projected quasi-subgradient method for constrained, nondifferentiable, quasi-convex multiobjective minimization problems. Unlike existing approaches that rely on Lipschitz continuity, our method only requires Hölder continuity of the objective components, thereby covering a broader class of quasi-convex functions. Under these assumptions, we establish convergence of the generated sequence to a Pareto optimal solution and derive a sublinear rate of convergence that explicitly depends on the Hölder parameters, recovering the Lipschitz case as a special instance. The method is simple to implement, robust to nondifferentiability, and theoretically well-defined. Numerical experiments including application to portfolio optimization, electric vehicle charging network optimization and smart grid energy management are provided. Dolan-Moré performance profiles indicate that the proposed method outperforms.