Foreword: Special issue on nonlinear programming, variational inequalities, and stochastic programming

2007 ◽  
Vol 117 (1-2) ◽  
pp. 1-4 ◽  
Author(s):  
Jong-Shi Pangc ◽  
Daniel Ralph
Keyword(s):  
Nonlinear Programming ◽  
Stochastic Programming ◽  
Variational Inequalities ◽  
Special Issue

scholarly journals Active‐Set Newton Methods and Partial Smoothness

2020 ◽  
Author(s):  
Adrian S. Lewis ◽  
Calvin Wylie
Keyword(s):  
Nonlinear Programming ◽  
Variational Inequalities ◽  
Finite Time ◽  
Optimization Algorithms ◽  
Newton Methods ◽  
Active Set ◽  
Local Algorithms ◽  
Partial Smoothness ◽  
Analogous Behavior ◽  
Partly Smooth

Diverse optimization algorithms correctly identify, in finite time, intrinsic constraints that must be active at optimality. Analogous behavior extends beyond optimization to systems involving partly smooth operators, and in particular to variational inequalities over partly smooth sets. As in classical nonlinear programming, such active‐set structure underlies the design of accelerated local algorithms of Newton type. We formalize this idea in broad generality as a simple linearization scheme for two intersecting manifolds.

scholarly journals Special Issue: Topics in Stochastic Programming

2022 ◽  
Author(s):  
Tito Homem-de-Mello ◽  
Miloš Kopa ◽  
David P. Morton
Keyword(s):  
Stochastic Programming ◽  
Special Issue

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.

Foreword: Special issue on nonlinear convex optimization and variational inequalities

2007 ◽  
Vol 116 (1-2) ◽  
pp. 1-3 ◽  
Author(s):  
Hedy Attouch ◽  
Roberto Cominetti ◽  
Marc Teboulle
Keyword(s):  
Convex Optimization ◽  
Variational Inequalities ◽  
Special Issue
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