Hierarchical Multilevel Multi-leader Multi-follower Problem Multi-parametric Solution Approach

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Hierarchical multilevel multi-leader multi-follower games are non-cooperative decisionrnproblems in which multiple decision-makers of equal status in the upperlevelrnandmultiple decision-makers of equal status are involved at each of the lowerlevelsrnof the hierarchy. Much of solution methods proposed so far on the topic arerneither model specific which may work only for a particular sub-class of problems orrnare based on some strong assumptions and mainly for two level cases. In this dissertationrnwe have proposed a multi-parametric programming based solution approachrnfor hierarchical multilevel multi-leader multi-follower games in which the objectivernfunctions contain separable and non-separable terms (but the non-separable termsrncan be written as a factor of two functions, a function which depends on other levelrndecision variables and a function which is common to all objectives across the samernlevel) and shared constraint. The proposed solution approach transforms a hierarchicalrnmultilevel multi-leader multi-follower game into multilevel game involvingrna single decision maker at each level of the hierarchy. In addition, a solutionrnalgorithm for bilevel optimization problems whose lower-level problem involvesrnconvex nonlinear constraints is also developed. The solution algorithm recasts thernlower-level problem as a multi-parametric problem and employs an equivalent barrierrnproblem reformulation. The solution obtained with this method is shown to bernexact if the lower-level problem and the nonlinear constraints can be expressed byrna polynomial of utmost degree three with followers’ variable and upto quadratic inrnthe variable of the leader.

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Hierarchical Multilevel Multi-leader Multi-follower Problem Multi-parametric Solution Approach

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