Power grid vulnerability analysis is often performed through solving a bi-level optimization problem, which, if solved to optimality, yields the most destructive interdiction plan with the worst loss. As one of the most effective operations to mitigate deliberate outages or attacks, transmission line switching recently has been included and modeled by a binary variable in the lower level decisi...

Model-Agnostic Meta-Learning (MAML), a popular gradient-based meta-learning framework, assumes that the contribution of each task or instance to meta-learner is equal.Hence, it fails address domain shift between base and novel classes in few-shot learning. In this work, we propose robust algorithm, NESTEDMAML, which learns assign weights training tasks instances. We con-sider as hyper-parameter...

Mathematical programmes with equilibrium constraints (MPECs) constitute important modelling tools for network flow problems, as they place 'what-if' analyses in a proper mathematical framework. We consider a class of stochastic MPEC traffic models that explicitly incorporate possible uncertainties in travel costs and demands. In stochastic programming terminology, we consider 'here-and-now' mod...

 We wish to classify a high-dimensional observation as belonging to one of two classes. Toward that end, we present a bi-level optimization procedure for maximizing, conditional on observed training data and subject to maximum likelihood constraints, a measure of the -dimensional class-conditional probability density estimate separation for . The separation optimization involves traversal of a...

ABSTRACT. Bi-level programming problems are an important type of multi-variable and double-layer programming problems. These problems appear everywhere especially in the industrial, supply-chain, and marketing programming applications. In this work, two new original approaches are proposed to solve bi-level quadratic programming problems in different cases: the so-called ergodic branch-and-boun...

Available transfer capability (ATC) is the transfer capability remaining in the physical transmission network for further commercial activity over and above already committed uses which needs to be posted in the electricity market to facilitate competition. ATC evaluation is a complicated task including the determination of total transfer capability (TTC) and existing transfer capability (ETC)....

Some recent works in machine learning and computer vision involve the solution of a bilevel optimization problem. Here the solution of a parameterized lower-level problem binds variables that appear in the objective of an upper-level problem. The lower-level problem typically appears as an argmin or argmax optimization problem. Many techniques have been proposed to solve bi-level optimization p...