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Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
Generally, combinatorial design concerns with the arrangement of a finite set of elements into patterns (subsets, words, arrays) according to specified rules. The usefulness of this design method is that the number of input combination can…
Recently, machine learning has been used in every possible field to leverage its amazing power. For a long time, the net-working and distributed computing system is the key infrastructure to provide efficient computational resource for…
In this paper, we introduce a conceptual framework that model human social networks as an undirected dot-product graph of independent individuals. Their relationships are only determined by a cost-benefit analysis, i.e. by maximizing an…
Power systems are susceptible to natural threats including hurricanes and floods. Modern power grids are also increasingly threatened by cyber attacks. Existing approaches that help improve power system security and resilience may not be…
We introduce a general and comprehensive model for the design and optimization of Virtual Networks, and for the related concept of Network Slicing. The model is flexible, so that by adjusting some of its elements, it can accommodate many…
Over the last decade, wireless networks have experienced an impressive growth and now play a main role in many telecommunications systems. As a consequence, scarce radio resources, such as frequencies, became congested and the need for…
We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…
The design and optimization of wireless networks have mostly been based on strong mathematical and theoretical modeling. Nonetheless, as novel applications emerge in the era of 5G and beyond, unprecedented levels of complexity will be…
Deep structured models are widely used for tasks like semantic segmentation, where explicit correlations between variables provide important prior information which generally helps to reduce the data needs of deep nets. However, current…
This work develops an LLM-based optimization framework ensuring strict constraint satisfaction in network optimization. While LLMs possess contextual reasoning capabilities, existing approaches often fail to enforce constraints, causing…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
The study of network formation is pervasive in economics, sociology, and many other fields. In this paper, we model network formation as a `choice' that is made by nodes in a network to connect to other nodes. We study these `choices' using…
Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges or as a…
Real networks exhibit nontrivial topological features such as heavy-tailed degree distribution, high clustering, and small-worldness. Researchers have developed several generative models for synthesizing artificial networks that are…
Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by…
Adaptive networks are a novel class of dynamical networks whose topologies and states coevolve. Many real-world complex systems can be modeled as adaptive networks, including social networks, transportation networks, neural networks and…
Deep learning models have proven to be exceptionally useful in performing many machine learning tasks. However, for each new dataset, choosing an effective size and structure of the model can be a time-consuming process of trial and error.…
This paper considers the problem of designing a dynamical system to solve constrained optimization problems in a distributed way and in an anytime fashion (i.e., such that the feasible set is forward invariant). For problems with separable…