# Second- and First-Order Optimality Conditions in Vector Optimization

@article{Ivanov2013SecondAF, title={Second- and First-Order Optimality Conditions in Vector Optimization}, author={Vsevolod I. Ivanov}, journal={Int. J. Inf. Technol. Decis. Mak.}, year={2013}, volume={14}, pages={747-768} }

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. In the necessary conditions, we suppose that the objective function and the active constraints are continuously differentiable. We introduce notions of KTSP-invex problem and second-order KTSP-invex one. We obtain that the vector problem is (second-order) KTSP-invex if and only if for every triple $(\bar{x},\bar…

## 7 Citations

### Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications

- 2015

Mathematics

J. Optim. Theory Appl.

The inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints is considered, and second-order necessary optimality conditions of Karush–Kuhn–Tucker type are obtained for weak efficiency.

### Second-Order Optimality Conditions for Vector Problems with Continuously Fréchet Differentiable Data and Second-Order Constraint Qualifications

- 2015

Mathematics

Journal of Optimization Theory and Applications

In the present paper, we consider the inequality constrained vector problem with continuously Fréchet differentiable objective functions and constraints. We obtain second-order necessary optimality…

### On Necessary Optimality Conditions for Nonsmooth Vector Optimization Problems with Mixed Constraints in Infinite Dimensions

- 2016

Mathematics

Applied Mathematics & Optimization

In this note, we develop first- and second-order necessary optimality conditions for local weak solutions in nonsmooth vector optimization problems subject to mixed constraints in…

### On Necessary Optimality Conditions for Nonsmooth Vector Optimization Problems with Mixed Constraints in Infinite Dimensions

- 2018

Mathematics

In this note, we develop first- and second-order necessary optimality conditions for local weak solutions in nonsmooth vector optimization problems subject to mixed constraints in…

### On the Fritz John saddle point problem for differentiable multiobjective optimization

- 2016

Mathematics

OPSEARCH

In this contribution, the relationship between saddle points of Lagrangian functions associated with the inequality constrained multiobjective optimization problem and Fritz John critical points are…

### On the Fritz John saddle point problem for differentiable multiobjective optimization

- 2016

Mathematics

In this contribution, the relationship between saddle points of Lagrangian functions associated with the inequality constrained multiobjective optimization problem and Fritz John critical points are…

### Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

- 2022

Mathematics, Computer Science

Numerical Functional Analysis and Optimization

An algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems is proposed.

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