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A class of evolution variational inequalities (EVIs), which comprises ordinary differential equations (ODEs) coupled with variational inequalities (VIs) associated with time-varying set-valued mappings, is proposed in this paper. We first…
This paper considers optimal control of dynamical systems which are represented by nonlinear stochastic differential equations. It is well-known that the optimal control policy for this problem can be obtained as a function of a value…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
A piecewise constant Mayer cost function is used to model optimal control problems in which the state space is partitioned into several regions, each having its own Mayer cost value. In such a context, the standard numerical methods used in…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in mathematical programming, including…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
The main feature of the Dynamic Multi-objective Optimization Problems (DMOPs) is that optimization objective functions will change with times or environments. One of the promising approaches for solving the DMOPs is reusing the obtained…
One of the challenging scientific computing problems is topology optimization, where searching through the combinatorially complex configurations and solving the constraints of partial differential equations need to be done simultaneously.…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…
Inverse optimal control (IOC) is a promising paradigm for learning and mimicking optimal control strategies from capable demonstrators, or gaining a deeper understanding of their intentions, by estimating an unknown objective function from…
Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…
This paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [Ararat et al. 2022, Doerfler…
This work establishes sensitivities of the solution of an optimal control problem (OCP) and a corresponding quantity of interest (QoI) to perturbations in a state/control-dependent component function that appears in the governing ODEs and…
We consider a stochastic Inverse Variational Inequality (IVI) problem defined by a continuous and co-coercive map over a closed and convex set. Motivated by the absence of performance guarantees for stochastic IVI, we present a…
A well-posed initial-boundary value problem is formulated for the model problem of the vector wave equation subject to the divergence-free constraint. Existence, uniqueness and stability of the solution is proved by reduction to a system…
This paper revisits the problem of optimal control law design for linear systems using the global optimal control framework introduced by Vadim Krotov. Krotov's approach is based on the idea of total decomposition of the original optimal…
Stiff systems of ordinary differential equations (ODEs) and sparse training data are common in scientific problems. This paper describes efficient, implicit, vectorized methods for integrating stiff systems of ordinary differential…
Optimization of constrained quantum control problems powers quantum technologies. This task becomes very difficult when these control problems are nonconvex and plagued with dense local extrema. For such problems current optimization…
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-convex, continuous, and possibly non-smooth objective functions…