Interpretable Multi-Task Learning can be expressed as learning a sparse graph of the task relationship based on prediction performance learned models. Since many natural phenomenon exhibit structures, enforcing sparsity models reveals underlying relationship. Moreover, different sparsification degrees from fully connected uncover various types like cliques, trees, lines, clusters or disconnecte...

We present two bilevel programming formulations for the aircraft deconfliction problem: one based on speed regulation in k dimensions, other heading angle changes 2 dimensions. propose three reformulations of each problem KKT conditions and different duals lower-level subproblems. also a cut generation algorithm to solve formulations. Finally, we computational results variety instances.

Although leader-follower games have been around for quite some time in economics and game theory, their integration into the realm of optimization and operations research is recent. In this paper, we provide an overview of research in bilevel programming that was initiated at the University of Montreal and led to a large scale application in the field of revenue management.

This paper propose a self adaptive penalty function for solving constrained value-bilevel programming problem using genetic algorithm. This self adaptive penalty function based genetic algorithm both used in the higher level and the lower level problem's solving process. In the constraint handing method, a new fitness value called distance value, in the normalized fitness-constraint violation s...

The co-operative formulation of a nonlinear bilevel program involving nonconvex functions is considered and two equivalent reformulations to simpler programs are presented. It is shown that previous literature proposals for the global solution of such programs are not generally valid for nonconvex inner programs and several consequences of nonconvexity in the inner program are identified. In pa...

Enterprise-wide supply chain planning problems inherently exhibit multi-level decision network structures, where for example, one level may correspond to a local plant control/scheduling/planning problem and another level to a plant-wide planning/distribution network problem. Such multi-level decision network structures can be mathematically represented using multi-level mathematical programmin...

Basic bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his/her objective, subject to a set of constraints and his/her follower’s solution, and the follower at the lower level tries to find an optimized strategy according to each of possible decisions made by the leader. Three issues may be involved in a basic bilevel d...

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