Recently, by using the derivatives of scalarized maps, associated with a vector optimization problem, new multiplier rules have been proven. The first objective of this paper is to show that those rules do not hold in infinite dimensional setting without imposing additional restrictions, even when the ordering cone has...
We prove that the weak Pareto solution set of a multi-objective optimization problem with convex polynomial objectives and constraints is connected, assuming neither boundedness of the constraint set nor a constraint qualification. Since this set is semi-algebraic, its connectedness implies that it is path-connected wh...
We consider five basic optimality principles for a general multiobjective optimization problem with convex and nonconvex partial objectives. We introduce a generalization of the concept of trade-off directions defining them via some optimal surface of appropriate cones. In both cases, we link optimality and generalized...
Convexity and generalized convexity play a central role in mathematical programming for duality results and in order to characterize the solutions set. In this paper, taking in mind Craven's notion of K-invexity function (when K is a cone in \mathbb{R}^n R n ) and Martin's notion of Karush-Kuh...
We introduce Envelopt, a globally convergent iterative framework for a broad class of structured optimization problems where a smooth objective is augmented by a nonsmooth convex regularizer composed with a smooth mapping, and the variables are subject to general smooth constraints. All smooth functions may be nonconve...
In our previous work [8], we proposed two novel mechanisms for generating closed convex cones: one based on systems of inequalities and the other on support functions, together with explicit characterizations of the associated dual and polar cones. Building upon these results, the present paper develops a strengthened...
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