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We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Partial-differential-equation (PDE)-constrained optimization is a well-worn technique for acquiring optimal parameters of systems governed by PDEs. However, this approach is limited to providing a single set of optimal parameters per…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
In this paper, we introduce various mechanisms to obtain accelerated first-order stochastic optimization algorithms when the objective function is convex or strongly convex. Specifically, we extend the Catalyst approach originally designed…
We propose a new distributed optimization algorithm for solving a class of constrained optimization problems in which (a) the objective function is separable (i.e., the sum of local objective functions of agents), (b) the optimization…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
Evolutionary algorithms have been widely applied for solving dynamic constrained optimization problems (DCOPs) as a common area of research in evolutionary optimization. Current benchmarks proposed for testing these problems in the…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
Autonomous agents are limited in their ability to observe the world state. Partially observable Markov decision processes (POMDPs) formally model the problem of planning under world state uncertainty, but POMDPs with continuous actions and…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
In performative stochastic optimization, decisions can influence the distribution of random parameters, rendering the data-generating process itself decision-dependent. In practice, decision-makers rarely have access to the true…
Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often…
We develop and analyze a set of new sequential simulation-optimization algorithms for large-scale multi-dimensional discrete optimization via simulation problems with a convexity structure. The "large-scale" notion refers to that the…
Many safety-critical real-world problems, such as autonomous driving and collaborative robots, are of a distributed multi-agent nature. To optimize the performance of these systems while ensuring safety, we can cast them as distributed…