scholarly journals Quasi-convex functions and applications to optimality conditions in nonlinear programming

2001 ◽  
Vol 14 (2) ◽  
pp. 241-244
Author(s):  
A. Hassouni ◽  
A. Jaddar
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions

scholarly journals A Class of SemilocalE-Preinvex Functions and Its Applications in Nonlinear Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Hehua Jiao ◽  
Sanyang Liu ◽  
Xinying Pai
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Convex Functions ◽  
Convex Set ◽  
Basic Properties ◽  
New Class ◽  
Duality Results ◽  
Invex Set ◽  
Preinvex Functions ◽  
Class Of Functions

A kind of generalized convex set, called as local star-shapedE-invex set with respect toη,is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocalE-preinvex functions, which is a generalization of semi-E-preinvex functions and semilocalE-convex functions, is introduced. Simultaneously, some of its basic properties are discussed. Furthermore, as its applications, some optimality conditions and duality results are established for a nonlinear programming.

scholarly journals SOME PROPERTIES OF EXPONENTIALLY PREINVEX FUNCTIONS

2019 ◽  
pp. 941
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Optimality Conditions ◽  
Convex Functions ◽  
New Concepts ◽  
Preinvex Functions

In this paper, we introduce some new concepts of the exponentially preinvex functions. We investigate several properties of the exponentially preinvex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational-like inequalities. Several interesting results characterizing the exponentially preinvex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results.

scholarly journals Mixed-type duality for multiobjective fractional variational control problems

2005 ◽  
Vol 2005 (1) ◽  
pp. 109-124 ◽  
Author(s):  
Raman Patel
Keyword(s):  
Nonlinear Programming ◽  
Convex Functions ◽  
Mixed Type ◽  
Efficient Solutions ◽  
Control Problems ◽  
Duality Results ◽  
Finite Dimensional ◽  
Duality Relations ◽  
Mixed Type Duality ◽  
Convexity Assumptions

The concept of mixed-type duality has been extended to the class of multiobjective fractional variational control problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained forρ-convex (generalizedρ-convex) functions. The results generalize a number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions.

scholarly journals Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C1-data

1999 ◽  
Vol 40 (3) ◽  
pp. 403-420 ◽  
Author(s):  
V. Jeyakumar ◽  
X. Wang
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Second Order ◽  
Second Order Optimality Conditions ◽  
Differentiable Functions ◽  
Continuous Maps ◽  
Mathematical Programming Problems ◽  
Approximate Hessian

AbstractIn this paper, we present generalizations of the Jacobian matrix and the Hessian matrix to continuous maps and continuously differentiable functions respectively. We then establish second-order optimality conditions for mathematical programming problems with continuously differentiable functions. The results also sharpen the corresponding results for problems involving C1.1-functions.

On second-order optimality conditions for nonlinear programming

Optimization ◽  
2007 ◽  
Vol 56 (5-6) ◽  
pp. 529-542 ◽  
Author(s):  
R. Andreani ◽  
J. M. Martínez ◽  
M. L. Schuverdt
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Second Order ◽  
Second Order Optimality Conditions

Optimality conditions for sparse nonlinear programming

2017 ◽  
Vol 60 (5) ◽  
pp. 759-776 ◽  
Author(s):  
LiLi Pan ◽  
NaiHua Xiu ◽  
Jun Fan
Keyword(s):  
Nonlinear Programming ◽  
Optimality Conditions ◽  
Sparse Nonlinear Programming

scholarly journals Strongly log-biconvex Functions and Applications

2021 ◽  
pp. 1-23
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Optimality Conditions ◽  
Convex Functions

In this paper, we consider some new classes of log-biconvex functions. Several properties of the log-biconvex functions are studied. We also discuss their relations with convex functions. Several interesting results characterizing the log-biconvex functions are obtained. New parallelogram laws are obtained as applications of the strongly log-biconvex functions. Optimality conditions of differentiable strongly log-biconvex are characterized by a class of bivariational inequalities. Results obtained in this paper can be viewed as significant improvement of previously known results.

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