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We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
The Reactive Optimal Power Flow (ROPF) problem consists in computing an optimal power generation dispatch for an alternating current transmission network that respects power flow equations and operational constraints. Some means of action…
Spectral Clustering as a relaxation of the normalized/ratio cut has become one of the standard graph-based clustering methods. Existing methods for the computation of multiple clusters, corresponding to a balanced $k$-cut of the graph, are…
In this paper, a non-linear p-robust hub location problem is extended to a risky environment where augmented chance constraint with a min-max regret form is employed to consider network risk as one of the objectives. The model considers…
The optimal reactive power dispatch (ORPD) problem is an alternating current optimal power flow (ACOPF) problem where discrete control devices for regulating the reactive power, such as shunt elements and tap changers, are considered. The…
The Alternating Current Optimal Transmission Switching (ACOTS) problem incorporates line switching decisions into the AC Optimal Power Flow (ACOPF) framework, offering well-known benefits in reducing operational costs and enhancing system…
Higher levels of renewable electricity generation increase uncertainty in power system operation. To ensure secure system operation, new tools that account for this uncertainty are required. In this paper, we formulate a chance-constrained…
Decentralized optimization algorithms are important in different contexts, such as distributed optimal power flow or distributed model predictive control, as they avoid central coordination and enable decomposition of large-scale problems.…
High penetration of renewable energy sources and the increasing share of stochastic loads require the explicit representation of uncertainty in tools such as the optimal power flow (OPF). Current approaches follow either a linearized…
Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation/coherence threshold have been recently proposed as efficient analog simulators of 2-local spin…
In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…
We study a mixed integer linear program with m integer variables and k non-negative continuous variables in the form of the relaxation of the corner polyhedron that was introduced by Andersen, Louveaux, Weismantel and Wolsey [Inequalities…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
This paper presents an efficient algorithm for the approximation of the rank-one convex hull in the context of nonlinear solid mechanics. It is based on hierarchical rank-one sequences and simultaneously provides first and second derivative…
Recent works have established the utility of sparsity-promoting norms for extracting spatially-localized instability mechanisms in fluid flows, with possible implications for flow control. However, these prior works have focused on linear…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
Clustering under pairwise constraints is an important knowledge discovery tool that enables the learning of appropriate kernels or distance metrics to improve clustering performance. These pairwise constraints, which come in the form of…
Convex relaxations of the AC Optimal Power Flow (OPF) problem are essential not only for identifying the globally optimal solution but also for enabling the use of OPF formulations in Bilevel Programming and Mathematical Programs with…
It is a crucial problem how to heat oil and save running cost for crude oil transport. This paper strictly formulates such a heated oil pipeline problem as a mixed integer nonlinear programming model. Nonconvex and convex continuous…
Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and…