A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduct...

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Vydáno v:Journal of computational and applied mathematics Ročník 146; číslo 1; s. 99 - 113
Hlavní autoři: Xu, Jiuping, Li, Jun
Médium: Journal Article Konferenční příspěvek
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 01.09.2002
Elsevier
Témata:
(Stochastic) Multiple quadratic-linear programming
(Weakly) Efficient solution
Applied sciences
Exact sciences and technology
Interactive algorithm
Mathematical programming
Operational research and scientific management
Operational research. Management science
Portfolio selection model
(Stochastic) Multiple quadratic-linear programming
Interactive algorithm
(Weakly) Efficient solution
Portfolio selection model
Selection problem
Necessary and sufficient condition
Weight function
Optimization method
Multiobjective programming
Linear programming
Objective function
Quadratic programming
Random variable
Constrained optimization
Stochastic programming
ISSN:0377-0427, 1879-1778
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Shrnutí:In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables’ expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/S0377-0427(02)00421-1