Directional derivative of the marginal function in nonlinear programming

1984 ◽  
pp. 110-126 ◽  
Author(s):  
Robert Janin
Keyword(s):  
Nonlinear Programming ◽  
Directional Derivative ◽  
Marginal Function

On variational inequalities and nonlinear programming problem

2008 ◽  
Vol 45 (4) ◽  
pp. 483-491
Author(s):  
Vsevolod Ivanov
Keyword(s):  
Variational Inequality ◽  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Programming Problem ◽  
Directional Derivative ◽  
Nonlinear Programming Problem ◽  
Solution Sets ◽  
Minty Variational Inequality ◽  
Stampacchia Variational Inequality ◽  
Dini Directional Derivative

In this paper the Stampacchia variational inequality, the Minty variational inequality, and the respective nonlinear programming problem are investigated in terms of the lower Dini directional derivative. We answer the questions which are the largest classes of functions such that the solution sets of each pair of these problems coincide.

On The Marginal Function in Nonlinear Programming

1984 ◽  
Vol 9 (2) ◽  
pp. 208-221 ◽  
Author(s):  
Bernhard Gollan
Keyword(s):  
Nonlinear Programming ◽  
Marginal Function

scholarly journals Sufficient Optimality and Sensitivity Analysis of a Parameterized Min-Max Programming

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Huijuan Xiong ◽  
Yu Xiao ◽  
Chaohong Song
Keyword(s):  
Sensitivity Analysis ◽  
Objective Function ◽  
Directional Derivative ◽  
Second Order ◽  
Marginal Function ◽  
Feasible Set ◽  
Second Order Directional Derivative ◽  
Computation Formula ◽  
Clarke’S Subdifferential

Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max programming is discussed first. Moreover, under a convex assumption on the objective function, a subdifferential computation formula of the marginal function is obtained. The assumptions are satisfied naturally for some application problems. Moreover, the formulae based on these assumptions are concise and convenient for algorithmic purpose to solve the applications.

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