7 research outputs found
Optimality and duality for generalized fractional programming involving nonsmooth (F, Ï)-convex functions
AbstractUsing a parametric approach, we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing (F, Ï)-convex function
On nonsmooth multiobjective fractional programming problems involving (p, r)â Ï â(η ,Ξ)- invex functions
A class of multiobjective fractional programming problems (MFP) is considered where the involved functions are locally Lipschitz. In order to deduce our main results, we introduce the definition of (p,r)âÏ â(η,Ξ)-invex class about the Clarke generalized gradient. Under the above invexity assumption, sufficient conditions for optimality are given. Finally, three types of dual problems corresponding to (MFP) are formulated, and appropriate dual theorems are proved
A derivative-free approach to constrained multiobjective nonsmooth optimization
open3noopenLiuzzi, G.; Lucidi, S.; Rinaldi, F.Liuzzi, G.; Lucidi, S.; Rinaldi, Francesc
A Linesearch-based Derivative-free Approach for Nonsmooth Optimization
In this paper, we propose new linesearch-based methods for nonsmooth optimization problems
when first-order information on the problem functions is not available. In the first part, we describe
a general framework for bound-constrained problems and analyze its convergence towards
stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider
inequality constrained optimization problems where both objective function and constraints can
possibly be nonsmooth. In this case, we first split the constraints into two subsets: difficult general
nonlinear constraints and simple bound constraints on the variables. Then, we use an exact
penalty function to tackle the difficult constraints and we prove that the original problem can
be reformulated as the bound-constrained minimization of the proposed exact penalty function.
Finally, we use the framework developed for the bound-constrained case to solve the penalized
problem, and we prove that every accumulation point of the generated sequence of points is a
stationary points of the original constrained problem.
In the last part of the paper, we report extended numerical results on both bound-constrained
and nonlinearly constrained problems, showing the effectiveness of our approach when compared
to some state-of-the-art codes from the literature