17 citations · 64 across the 12 of their papers we have counts for
13 papers
Optimality conditions via exact penalty functions
Vsevolod Ivanov Ivanov
In this paper, we obtain optimality conditions for the problem with inequality, equality and closed set constraints in terms of the lower Hadamard derivative. The results are obtai…
Characterizations of Pseudolinear and Semi-strictly Quasilinear Functions
Vsevolod I. Ivanov
In this paper we obtain several new complete characterizations of pseudolinear functions. Two of the results are of first-order and one is derivative free. All results are derived…
Multiobjective Programming and Weighting Scalar Problem
Vsevolod I. Ivanov
In this work is discussed the paper by Osuna-Gomez, Beato-Moreno and Rufian-Lizana, Generalized convexity in multiobjective programming: J. Math. Anal. Appl., v. 233 (1999) pp. 205…
First and Second Order Necessary and Sufficient Optimality Conditions of Fritz John Type for Vector Problems over Cones
Vsevolod I. Ivanov
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…
Characterizations of Pseudoconvex Functions
Vsevolod Ivanov Ivanov
A differentiable function is pseudoconvex if and only if its restrictions over straight lines are pseudoconvex. A differentiable function depending on one variable, defined on some…
Characterizations of Solution Sets of Fréchet Differentiable Problems with Quasiconvex Objective Function
Vsevolod Ivanov Ivanov
In this paper, we study some problems with continuously differentiable quasiconvex objective function. We prove that exactly one of the following two alternatives holds: (I) the gr…
Higher-order optimality conditions with an arbitrary non-differentiable function
Vsevolod I. Ivanov
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…
Second-Order Optimality Conditions in Cone-Constrained Vector Optimization with Arbitrary Nondifferentiable Functions
Vsevolod I. Ivanov
In this paper, we introduce a new second-order directional derivative and a second-order subdifferential of Hadamard type for an arbitrary nondifferentiable function. We derive sev…
Optimality conditions with cone-generalized convex vector functions
Vsevolod I. Ivanov
The object of investigation in this paper are generalized convex vector nonlinear programming problems with cone constraints. We prove that a quasiconvex vector function is pseudoc…
Second-Order Karush-Kuhn-Tucker Optimality Conditions for Vector Problems with Continuously Differentiable Data and Second-Order Constraint Qualifications
Vsevolod I. Ivanov
Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivano…
Potentialities of Nonsmooth Optimization
Vsevolod Ivanov Ivanov
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-ord…
Optimality Conditions in Vector Optimization
Vsevolod I. Ivanov
In this paper we obtain second- and first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints.…
Second-order optimality conditions and Lagrange multiplier characterizations of the solution set in quasiconvex programming
Vsevolod I. Ivanov
Second-order optimality conditions for vector nonlinear programming problems with inequality constraints are studied in this paper. We introduce a new second-order constraint quali…