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In topology optimization, the state of structures is typically obtained by numerically evaluating a discretized PDE-based model. The degrees of freedom of such a model can be partitioned in free and prescribed sets to define the boundary…
In this paper, a class of large-scale distributed nonsmooth convex optimization problem over time-varying multi-agent network is investigated. Specifically, the decision space which can be split into several blocks of convex set is…
Complex systems display variability over a broad range of spatial and temporal scales. Some scales are unresolved due to computational limitations. The impact of these unresolved scales on the resolved scales needs to be parameterized or…
Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…
We consider a multiperiod stochastic capacitated facility location problem under uncertain demand and budget in each period. Using a scenario tree representation of the uncertainties, we formulate a multistage stochastic integer program to…
The stochastic gradient (SG) method can minimize an objective function composed of a large number of differentiable functions, or solve a stochastic optimization problem, to a moderate accuracy. The block coordinate descent/update (BCD)…
Day-ahead scheduling of electricity generation or unit commitment is an important and challenging optimization problem in power systems. Variability in net load arising from the increasing penetration of renewable technologies have…
This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage…
We study the problem of optimal state-feedback tracking control for unknown discrete-time deterministic systems with input constraints. To handle input constraints, state-of-art methods utilize a certain nonquadratic stage cost function,…
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state DP problem which satisfies the Principle of Optimality and…
We derived a number of numerical methods to treat biomolecular systems with multiple time scales. Based on the splitting of the operators associated with the slow-varying and fast-varying forces, new multiple time-stepping (MTS) methods are…
Time-evolving or temporal graphs gain more and more popularity when studying the behavior of complex networks. In this context, the multistage view on computational problems is among the most natural frameworks. Roughly speaking, herein one…
Increasing effort is put into the development of methods for learning mechanistic models from data. This task entails not only the accurate estimation of parameters but also a suitable model structure. Recent work on the discovery of…
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
The multiresponse surface problem is modelled as one of multiobjective stochastic optimisation, and diverse solutions are proposed. Several crucial differences are highlighted between this approach and others that have been proposed.…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere…
Stochastic optimization problems often involve data distributions that change in reaction to the decision variables. This is the case for example when members of the population respond to a deployed classifier by manipulating their features…