An elementary survey of general duality theory in mathematical programming

1981 ◽  
Vol 21 (1) ◽  
pp. 241-261 ◽  
Author(s):  
Jorgen Tind ◽  
Laurence A. Wolsey
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
General Duality ◽  
General Duality Theory

scholarly journals Duality in finite dimensional complex space

1978 ◽  
Vol 18 (1) ◽  
pp. 65-75
Author(s):  
C.H. Scott ◽  
T.R. Jefferson
Keyword(s):  
Quadratic Programming ◽  
Duality Theory ◽  
Complex Space ◽  
Optimization Problems ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Mathematical Programs ◽  
Finite Dimensional ◽  
General Duality ◽  
General Duality Theory

The idea of duality is now a widely accepted and useful idea in the analysis of optimization problems posed in real finite dimensional vector spaces. Although similar ideas have filtered over to the analysis of optimization problems in complex space, these have mainly been concerned with problems of the linear and quadratic programming variety. In this paper we present a general duality theory for convex mathematical programs in finite dimensional complex space, and, by means of an example, show that this formulation captures all previous results in the area.

scholarly journals A GENERAL DUALITY THEORY FOR CLONES

2013 ◽  
Vol 23 (03) ◽  
pp. 457-502 ◽  
Author(s):  
SEBASTIAN KERKHOFF
Keyword(s):  
Duality Theory ◽  
The Relationship ◽  
General Duality ◽  
General Duality Theory

Inspired by work of Mašulović, we outline a general duality theory for clones that will allow us to dualize any given clone, together with its relational counterpart and the relationship between them. Afterwards, we put the approach to work and illustrate it by producing some specific results for concrete examples as well as some general results that come from studying the duals of clones in a rather abstract fashion.

Near unanimity: an obstacle to general duality theory

1995 ◽  
Vol 33 (3) ◽  
pp. 428-439 ◽  
Author(s):  
B. A. Davey ◽  
L. Heindorf ◽  
R. McKenzie
Keyword(s):  
Duality Theory ◽  
Near Unanimity ◽  
General Duality ◽  
General Duality Theory

A new duality theory for mathematical programming

Optimization ◽  
2011 ◽  
Vol 60 (8-9) ◽  
pp. 1209-1231 ◽  
Author(s):  
B.F. Svaiter
Keyword(s):  
Mathematical Programming ◽  
Duality Theory

scholarly journals Symmetric duality in complex spaces over cones

2021 ◽  
pp. 4-4
Author(s):  
Izhar Ahmad ◽  
Divya Agarwal ◽  
Kumar Gupta
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Optimization Theory ◽  
Second Order ◽  
Symmetric Duality ◽  
Polyhedral Cones ◽  
Complex Spaces ◽  
Duality Results ◽  
Duality Relations

Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

Characterizations of optimality for continuous convex mathematical programs. Part I. Linear constraints

1979 ◽  
Vol 21 (1) ◽  
pp. 37-44 ◽  
Author(s):  
C. H. Scott ◽  
T. R. Jefferson
Keyword(s):  
Mathematical Programming ◽  
Duality Theory ◽  
Linear Constraints ◽  
Lagrangian Formalism ◽  
Symmetric Duality ◽  
Mathematical Programs ◽  
Convex Functionals ◽  
Mathematical Programming Problems

AbstractRecently we have developed a completely symmetric duality theory for mathematical programming problems involving convex functionals. Here we set our theory within the framework of a Lagrangian formalism which is significantly different to the conventional Lagrangian. This allows various new characterizations of optimality.

scholarly journals ALEKSANDRAS ČYRAS AND OPTIMIZATION IN STRUCTURAL MECHANICS

2002 ◽  
Vol 8 (1) ◽  
pp. 4-33 ◽  
Author(s):  
Juozas Atkočiūnas ◽  
Algirdas Čižas
Keyword(s):  
Mathematical Programming ◽  
Mathematical Models ◽  
Duality Theory ◽  
Structural Mechanics ◽  
Research Results ◽  
Elastic Plastic

The study describes how in Lithuania (mostly in Vilnius) during some past decades a new trend of investigations in structural mechanics thanks to Aleksandras Čyras' (1927–2001) research and organisational activities has been developed. The main distinguished features of the trend are: application of mathematical programming, and especially the duality theory, to the optimization of elastic-plastic and other structures, formulation of mathematical models of structural mechanics problems, elaborating algorithms and programmes for their solution. The advantages of the research results are shown, a large information concerning the publication of the results and the evolution of investigations initiated by A. Čyras are presented.

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