On the Development and Future Aspects of Vector Optimization and MCDM

Proximal point algorithm for differentiable quasi-convex multiobjective optimization

“…Proof. Remind that from (15) in the proof of Lemma 3.3, we know that Ω := ∩ +∞ k=0 Ω k is a nonempty closed and convex set. Let x * ∈ Ω be given, consider…”

“…It is clear that a Pareto optimal point is also a weak Pareto optimal point but the converse is not true. These types of solution concepts have applications in the economy, industry, agriculture, and other fields, see [15].…”

Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

“…From utility theory, game theory, linear production theory and economics (see [20]), to portfolio optimization [11], jury selection [42], airline operations [9], radiation therapy [32], manpower planning [43] or reservoir management [1], among others, many real-life problems require taking several conflicting points of view into account. More than 500 applications between 1955 and 1986 can be found in [48].…”

Proximal point method for a special class of nonconvex multiobjective optimization functions

“…Usually, no single point will minimize all the given objective functions at once (i.e., there is no ideal minimizer), and so the concept of optimality has to be replaced by the concept of Pareto optimality or as we will see, Pareto-Clarke critical; see [11]. These types of problems have applications in the economy, industry, agriculture, and other fields; see [13]. [6] considered extensions of the proximal point method to the multiobjective setting, see also, [1,2,3,4,7,8,9,20] and references therein.…”