In bilevel optimization there are two decision makers, commonly denoted as the leader and the follower, and decisions are made in a hierarchical manner: the leader makes the first move, and then the follower reacts optimally to the leader's action. It is assumed that the leader can anticipate the decisions of the follower, hence the leader optimization task is a nested optimization problem that takes into consideration the follower's response.In this talk we focus on new branch-and-cut (B&C) algorithms for dealing with mixed-integer bilevel linear programs (MIBLPs). We first address a general case in which intersection cuts are used to cut off infeasible solutions. We then focus on a subfamily of MIBLPs in which the leader and the follower share a set of items, and the leader can select some of the items to inhibit their usage by the follower. Interdiction Problems, Blocker Problems, Critical Node/Edge Detection Problems are some examples of optimization problems that satisfy the later condition. We show that, in case the follower subproblem satisfies monotonicity property, a family of "interdiction-cuts" can be derived resulting in a more efficient B&C scheme.These new B&C algorithms consistently outperform (often by a large margin) alternative state-of-the-art methods from the literature, including methods that exploit problem specific information for special instance classes.

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Subjects were asked to match the speeds of two moving random-dot patterns seen through circular apertures. The speed of one pattern that moved horizontally toward the right of a computer screen changed continuously. The speed ofthis pattern represented the target. It was to be matched with the speed of the second pattern, which moved in the opposite direction. The subject con· trolled the speed of the second pattern by means of an isometric joystick. The distance between the apertures on the screen as well as the subject's distance from the screen served as experimental parameters. In this way, the effects of both spatial and temporal transients of pattern speed on human tracking performance were studied. To avoid anticipation by the subject, the amplitude and the frequency of the target pattern speed changed pseudorandomly. The accuracy with which the subject performed the matching task was influenced by the mean pattern speed and the parameters of the visual field. Within lower velocity ranges, the subject's sensitivity to the instantaneous speed differences varied according to Weber's law. The cross-correlation of the velocity time courses decreased when the mean speed of the target pattern was increased. Two stimulus parameters had a strong influence on the modulation of the correlation value: (1) the angular size of the stimulus on the retina and (2) the retinal eccentricity of the stimulus.

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A series of experiments were made on human performance in controlling optical relative movement. The aim was to test the influence of different kinds of relative movement on visually controlled steering tasks. Within adjacent displays on a computer screen random dot patterns moved in a fixed direction at continually changing speeds (Exp. 1) or at constant speed and in continually changing directions (Exp. 2). The subject was required to compensate for the unpredictable modulations of the pattern movement by means of an isometric joystick. The task was to adjust relative movements involving pure translation, symmetric convergence, divergence, or shear. Analysis indicated that the task performance was not dependent on the special kind of relative movement. However, performance was significantly higher in tasks where directionally disturbed relative movement had to be controlled compared to those situations in which relative movement varied with respect to speed.