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Optimization

Finding optimal solution for AI tasks ↓
Optimization

Research on the intersection of mathematics, computer science, and electrical engineering with a clear mission: find the optimal solution using advanced computational methods.

Mathematical optimization is a field of study on the intersection of mathematics, computer science, and electrical engineering that deals with the selection of a best element out of a set with respect to some criterion. The elements of the set are known as feasible solutions and the criterion is known as the objective function. Over the past couple of centuries, much of the work in mathematical optimization has focussed on the case of a convex, time-invariant set of feasible solutions and convex, time-invariant objective functions. This special case has become the work horse of machine learning, artificial intelligence, and most fields of engineering.

Research Focus

In our basic research, we focus study extensions towards (1) certain smooth, non-convex feasible sets and objective functions and (2) time-varying feasible sets and objective functions. The smooth non-convex problems, known as commutative and non-commutative polynomial optimization, have extensive applications in power systems, control theory, and machine learning, among others. The same applications can often benefit from the time-varying extensions.

Particular examples of this include our papers at AAAI 2019 (https://arxiv.org/abs/1809.05870) and AAAI 2020 (https://arxiv.org/abs/1809.03550), which deal with time-varying optimization, and our paper at AAAI 2021 (https://arxiv.org/abs/2006.07315), which deals with non-commutative polynomial optimization.

Optimization in Power Systems

Optimization in Power Systems

Recently, we have made major advances in optimization in power systems. This includes time-varying optimization with non-linear constraints of the alternating-current optimal power flows, as well as mixed-integer optimization in unit commitment.

Quantum Computing for Finance

Quantum Computing for Finance

There has been recently much interest in quantum computing, which holds the promise of speeding up numerous (but certainly not all) problems. We work with one of the world's largest financial institutions to explore the applications of quantum computing in the Financial Services Sector.

Polynomial Optimization in Structural Optimization

Polynomial Optimization in Structural Optimization

Polynomial optimization is an exciting area of research in optimization, just at the boundary between what is undecidable and what is efficiently solvable. Sustained progress in the field over the past two decades has enabled new applications within many areas of engineering. One novel application arises in structural engineering.

Research Results

Predictability and Fairness in Social Sensing

Predictability and Fairness in Social Sensing

The manner in which agents contribute to a social-computing platform (e.g., social sensing, social media) is often governed by distributed algorithms. We explore the guarantees available in situations, where fairness among the agents contributing to the platform is needed.

Warm-starting Quantum Optimization

Warm-starting Quantum Optimization

Many optimization problems in binary decision variables are hard to solve. In this work, we demonstrate how to leverage decades of research in classical optimization algorithms to warm-start quantum optimization algorithms. This allows the quantum algorithm to inherit the performance guarantees from the classical algorithm used in the warm-start.

Team Members

We are a diverse and balanced team comprised of students, researchers, and academics.

Hacking
human future

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