In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The characterization, already known single objective problems, are extended to by weighted sum and Chebyshev scalarizations. Using last scalarization, an algorithm obtaining approximation of the weak Pareto front whose effectiveness is illustrated solving a collection test ...

We establish sufficient optimality conditions for a class of nondifferentiable minimax fractional programming problems involving (F, α, ρ, d)convexity. Subsequently, we apply the optimality conditions to formulate two types of dual problems and prove appropriate duality theorems.

The aim of this paper is to study the problem of optimality of replicating strategies associated with pricing of American contingent claims in the Cox–Ross–Rubinstein model with proportional transaction costs. We show that a replication of the option is always possible. We give sufficient conditions for the existence of a replicating strategy which is optimal, and also show an example of an opt...

A minimal sufficient condition for global optimality involving the Darboux point, analogous to the minimal sufficient condition of local optimality involving the conjugate point, is presented. The Darboux point is then characterized for optimal control problems with linear dynamics, cost functionals with a general terminal state term and an integrand quadratic in the state and control, and gene...

Initially, second-order necessary and sufficient optimality conditions in terms of Hadamard type derivatives for the unconstrained scalar optimization problem φ(x)→ min, x ∈ R, are given. These conditions work with arbitrary functions φ, but they show inconsistency with the classical derivatives. This is a base to pose the question, whether the formulated optimality conditions remain true when ...

This paper deals with optimal impulsive control problems whose states are functions of bounded variation and impulsive controls are regular vector measures. The problem under consideration has multipoint state constraints. Examples of such problems may be found in mechanics, quantum electronics, robotics, ecology, economics, etc. Sufficient global optimality conditions involving certain sets of...

We consider a control constrained optimal control problem governed by a semilinear elliptic equation with nonlocal interface conditions. These conditions occur during the modeling of diffusegray conductive-radiative heat transfer. After stating first-order necessary conditions, second-order sufficient conditions are derived that account for strongly active sets. These conditions ensure local op...

Abstract Tanigawa (2016) showed that vertex-redundant rigidity of a graph implies its global in arbitrary dimension. We extend this result to periodic frameworks under fixed lattice representations. That is, we show if generic framework is vertex-redundantly rigid, the sense deletion single vertex orbit periodicity results periodically rigid framework, then it also globally rigid. Our proof sim...

In this paper, we investigate relation between weak subdifferential and augmented normal cone. We define augmented normal cone via weak subdifferential and vice versa. The necessary conditions for the global maximum are also stated. We produce preliminary properties of augmented normal cones and discuss them via the distance function. Then we obtain the augmented normal cone for the indicator f...