A Proximal Gradient Method for Multi-objective Optimization Problems Using Bregman Functions

In this paper, a globally convergent proximal gradient method is developed for convex multi-objective optimization problems using Bregman distance. The proposed method is free from any kind of a priori chosen parameters or ordering information of objective functions. At every iteration of the proposed method, a subproblem is solved to find a descent direction. This … Read more

Approximations for Pareto and Proper Pareto solutions and their KKT conditions

There has been numerous amount of studies on proper Pareto points in multiobjective optimization theory. Geoffrion proper points are one of the most prevalent form of proper optimality. Due to some convergence issues a restricted version of these proper points, Geoffrion proper points with preset bounds has been introduced recently. Since solution of any algorithm … Read more

On a Practical Notion of Geoffrion Proper Optimality in Multicriteria Optimization

Geoffrion proper optimality is a widely used optimality notion in multicriteria optimization that prevents exact solutions having unbounded trade-offs. As algorithms for multicriteria optimization usually give only approximate solutions, we analyze the notion of approximate Geoffrion proper optimality. We show that in the limit, approximate Geoffrion proper optimality may converge to solutions having unbounded trade-offs. … Read more

When is a gap function good for error bounds?

In this paper we survey some important classes of gap function for variational inequalities and also some recently introduced gap functions for generalized variational inequalities. A new gap function is proposed for generalized variational inequalities and error bound is developed. Error bounds are also developed for some particular classes of gap functions. In fact a … Read more

An Approximate Lagrange Multiplier Rule

In this paper, we show that for a large class of optimization problems, the Lagrange multiplier rule can be derived from the so-called approximate multiplier rule. In establishing the link between the approximate and the exact multiplier rule we first derive an approximate multiplier rule for a very general class of optimization problems using the … Read more