Pessimistic Bilevel Linear Optimization
Keywords:Pessimistic bilevel optimization, Bilevel linear optimization problem, Nonconvex optimization, Basic matrix, Optimal value function, Minimax problem, Local and global optimization, Solution algorithms, Enumeration algorithm, Descent algorithm
In this paper, we investigate the pessimistic bilevel linear optimization problem (PBLOP). Based on the lower level optimal value function and duality, the PBLOP can be transformed to a single-level while nonconvex and nonsmooth optimization problem. By use of linear optimization duality, we obtain a tractable and equivalent transformation and propose algorithms for computing global or local optimal solutions. One small example is presented to illustrate the feasibility of the method.
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