Duality theory and slackness conditions in multiobjective linear programming

Balbás, Alejandro; Jimenez, P.; Heras, Antonio

doi:10.1016/s0898-1221(99)00062-0

Cited by 7 publications

(1 citation statement)

References 9 publications

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“…Theory in LP concerns the concept of duality. The dual solutions can be used to measure the primal sensitivity with respect to changes in the independent term of the restrictions [6]. Solving in the area of LP problem normally used Simplex methods in which it could terminate, with returning a feasible solution or non-feasible one.…”

Section: Introductionmentioning

confidence: 99%

Symmetric matrices properties to duality in linear programming problem

Romli

Taufik

Saptari

et al. 2011

2011 Fourth International Conference on Modeling, Simulation and Applied Optimization

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Duality is one of the most important topics in optimization either a theoretical and algorithmic perspective. Optimization problem usually involved mathematical model. One of the applications widely used is Linear Programming. Linear functions applications are frequently used in production planning, networks, scheduling, and other application of a linear function subject to linear constraints. Extensive number of papers related with duality in optimization has been published. However, studies about the effect of different characteristics of randomly symmetric matrices in the duality in linear programming have not yet been discussed widely. This study addresses new findings which may contribute to advancement of LP theory and practice, particularly on the effects of various number of variables and different characteristics of matrices in LP problems to duality.

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Section: Introductionmentioning

confidence: 99%

Symmetric matrices properties to duality in linear programming problem

Romli

Taufik

Saptari

et al. 2011

2011 Fourth International Conference on Modeling, Simulation and Applied Optimization

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Nonlinear Multiobjective Programming

Engau

2011

Wiley Encyclopedia of Operations Research and Management Science

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This introductory treatment of the theory and methodology of nonlinear multiobjective programming offers an annotated bibliographic overview of various concepts and approaches to solve continuous deterministic multicriteria optimization problems. First, the notions of Pareto optimality, efficiency, and nondominance are discussed and then related to approximate, epsilon, and proper efficiency. Second, after highlighting similarities and pointing out differences to first‐ and second‐order optimality conditions in classical nonlinear programming, several other topics including duality and sensitivity are also mentioned. Third, a number of solution approaches and generating methods are described with a particular focus on scalarizations using objective aggregation, prioritization, and norm or distance minimization to some utopian reference point.

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Strictly feasible solutions and strict complementarity in multiple objective linear optimization

Mahdavi–Amiri

Sadaghiani

2016

4OR-Q J Oper Res

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Duality theory and slackness conditions in multiobjective linear programming

Cited by 7 publications

References 9 publications

Symmetric matrices properties to duality in linear programming problem

Symmetric matrices properties to duality in linear programming problem

Nonlinear Multiobjective Programming

Strictly feasible solutions and strict complementarity in multiple objective linear optimization

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