A reference direction approach to multiple objective quadratic-linear programming

Korhonen, Pekka; Yu, Guang Yuan

doi:10.1016/s0377-2217(96)00245-7

Cited by 29 publications

(14 citation statements)

References 6 publications

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“…The closest approaches of the vector optimization case (VQFP) are considered by Beato et al [3,4], Arévalo and Zapata [2], Konno and Inori [21], Rhode and Weber [34], Kornbluth and Steuer [24], Korhoen and Yu [22,23]. Using an iterative computational test, Beato et al [3,4] characterize the Pareto-efficient optimal point for the problem (VQFP), consisting of a linear and quadratic functions, and using the function linearization approach of Bector et al [6], some theoretical results are obtained.…”

Section: Quadratic Fractional Problem and Literature Reviewmentioning

confidence: 99%

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

Oliveira

Beato-Moreno

Moretti

et al. 2014

Journal of Applied Mathematics

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One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.

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Section: Quadratic Fractional Problem and Literature Reviewmentioning

confidence: 99%

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

Oliveira

Beato-Moreno

Moretti

et al. 2014

Journal of Applied Mathematics

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“…To our knowledge, no one knows how often multiple inverse images occur in problems like (4) and this should probably be kept in mind when interpreting results until more is known about the phenomenon. Since Markowitz, other specialized parametric quadratic programming algorithms for (4) have been developed by Best (1996), Korhonen and Yu (1997), Stein et al (2008), Niedermayer and Niedermayer (2010) and Hirschberger et al (2010), but like the critical line algorithm, only minimally complete efficient sets are computed. However, one thing is known from these exact algorithms and it is that the minimum-variance frontier; and hence, the nondominated set of (4) is made up of a series of parabolic segments in (variance, expected return) space.…”

Section: Multiple Objectives and Portfolio Optimizationmentioning

confidence: 99%

“…To our knowledge, no one knows how often multiple inverse images occur in problems like and this should probably be kept in mind when interpreting results until more is known about the phenomenon. Since Markowitz, other specialized parametric quadratic programming algorithms for have been developed by Best (), Korhonen and Yu (), Stein et al . (), Niedermayer and Niedermayer () and Hirschberger et al .…”

Section: Multiple Objectives and Portfolio Optimizationmentioning

confidence: 99%

Chinese Corporate Social Responsibility by Multiple Objective Portfolio Selection and Genetic Algorithms

Peng

et al. 2013

Multi Criteria Decision Anal

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In this paper, we study corporate social responsibility (CSR) in China through the prism of investments. We work with large stocks and assess their CSR performance from agency CSR data. We formulate Chinese CSR by a multiple objective extension of a traditional portfolio selection model and analytically solve the extension. We also solve the extension by a genetic algorithm and directly evaluate the algorithm's performance against the analytical solution. The multiple objective formulation is tested by randomly choosing nondominated portfolios with out-of-sample data to identify nondominated portfolios that outperform the 1/n portfolio (equally weighted portfolio).

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“…The above MCDM-based EMO approaches can also be used in an iterative manner with a DM, similar to the way suggested elsewhere [12,13]. In an semi-interactive EMO approach, some preference information (in terms of reference points or reference directions or others) can be obtained from the DM and an MCDM-based EMO algorithm can be employed to find a set of preferred Pareto-optimal solutions.…”

Section: Introductionmentioning

confidence: 99%

An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions

Deb

Sinha

Korhonen

et al. 2010

IEEE Trans. Evol. Computat.

192

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This paper suggests a preference based methodology, which incorporates an evolutionary multiobjective optimization algorithm to lead a decision-maker to the most preferred solution of her or his choice. The progress towards the most preferred solution is made by accepting preference based information progressively from the decision maker after every few generations of an evolutionary multiobjective optimization algorithm. This preference information is used to model a strictly increasing value function, which is used for the subsequent iterations of the EMO algorithm. In addition to the development of the value function which satisfies DM's preference information, the proposed progressively interactive EMO (PI-EMO) approach utilizes the constructed value function in directing EMO algorithm's search to more preferred solutions. This is accomplished using a preference-based domination principle and utilizing a preference based termination criterion. Results on two to five-objective optimization problems using the progressively interactive NSGA-II approach shows the simplicity of the proposed approach and its future promise. A parametric study involving the algorithm's parameters reveals interesting insights of parameter interactions and indicates useful parameter values. A number of extensions to this study are also suggested.

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A reference direction approach to multiple objective quadratic-linear programming

Cited by 29 publications

References 6 publications

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

Pareto Optimality Conditions and Duality for Vector Quadratic Fractional Optimization Problems

Chinese Corporate Social Responsibility by Multiple Objective Portfolio Selection and Genetic Algorithms

An Interactive Evolutionary Multiobjective Optimization Method Based on Progressively Approximated Value Functions

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