Related papers: Second-Order Optimality Conditions in Cone-Constra…
In this paper, we introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper extended real function. This derivative is harmonized with the classical higher-order Fr\'echet…
In this paper we derive new second-order optimality conditions for a very general set-constrained optimization problem where the underlying set may be nononvex. We consider local optimality in specific directions (i.e., optimal in a…
In this paper, we show that higher-order optimality conditions can be obtain for arbitrary nonsmooth function. We introduce a new higher-order directional derivative and higher-order subdifferential of Hadamard type of a given proper…
In this paper we study second-order optimality conditions for non-convex set-constrained optimization problems. For a convex set-constrained optimization problem, it is well-known that second-order optimality conditions involve the support…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
The paper is devoted to deriving novel second-order necessary and sufficient optimality conditions for local minimizers in rather general classes of nonsmooth unconstrained and constrained optimization problems in finite-dimensional spaces.…
In this paper, we obtain a new proof of Fritz John necessary optimality conditions for vector problems applying Kakutani fixed point theorem and Hadamard directional derivative. We also derive a similar proof of second-order Fritz John…
In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality…
In this paper, we present some second-order sufficient conditions in terms of the Demyanov-Pevnyi's second-order directional derivatives for efficiency of $C^1$ vector optimization problems with constraints. Our results improve and…
This paper explores local second-order weak sharp minima for a broad class of nonconvex optimization problems. We propose novel second-order optimality conditions formulated through the use of classical and lower generalized support…
This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is $C^2$-smooth, we show that strengthened…
This paper is devoted to the study of second order optimality conditions for strong local minimizers in the frameworks of unconstrained and constrained optimization problems in finite dimensions via subgradient graphical derivative. We…
This paper is concerned with necessary and sufficient second-order conditions for finite-dimensional and infinite-dimensional constrained optimization problems. Using a suitably defined directional curvature functional for the admissible…
This paper is concerned with the directional derivative of the value function for a very general set-constrained optimization problem under perturbation. Under reasonable assumptions, we obtain upper and lower estimates for the upper and…
Second-order optimality conditions are essential for nonsmooth optimization, where both the objective and constraint functions are Lipschitz continuous and second-order directionally differentiable. This paper provides no-gap second-order…
Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with…
In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator…
In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…
This paper develops a novel approach to necessary optimality conditions for constrained variational problems defined in generally incomplete subspaces of absolutely continuous functions. Our approach involves reducing a variational problem…
In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an…