最优化与控制
This paper develops a comprehensive extension of the $\Lambda$-set framework for optimal control, introducing second-order $\Lambda$-sets and generalizing the theory to non-smooth, hybrid, and stochastic hybrid systems. We first establish…
We introduce and analyze the stability of a class of event-triggered extremum-seeking algorithms designed to solve resource-aware, model-free, optimization problems. Leveraging recent advances in Lie-Bracket Averaging for hybrid systems, we…
Recent approaches for navigating among dynamic threat regions (i.e., weapon engagement zones) have focused on planning entire trajectories. Moreover, the allowance for penetration into these threat regions was based on heuristic…
We consider the problem of analyzing the probabilistic performance of first-order methods when solving convex optimization problems drawn from an unknown distribution only accessible through samples. By combining performance estimation…
In many applications of mathematical optimization, one may wish to optimize an objective function without access to its derivatives. These situations call for derivative-free optimization (DFO) methods. Among the most successful approaches…
In this paper we present an inexact zeroth-order method suitable for the solution nonsmooth and nonconvex stochastic composite optimization problems, in which the objective is split into a real-valued Lipschitz continuous stochastic…
This paper is devoted to a study of the controllability of a free-boundary problem for a class of one-dimensional degenerate parabolic equations with distributed controls, locally supported in space. We prove that for any $T>0$, if the…
Many numerical and learning algorithms rely on the solution of the Monge-Kantorovich problem and Wasserstein distances, which provide appropriate distributional metrics. While the natural approach is to treat the problem as an…
Dynamical formulations of optimal transport (OT) frame the task of comparing distributions as a variational problem which searches for a path between distributions minimizing a kinetic energy functional. In applications, it is frequently…
We present a novel approach to accelerate the Goemans-Williamson (GW) randomized rounding procedure for quadratic unconstrained binary optimization (QUBO) problems. Instead of solving the conventional semi-definite programming (SDP)…
Newton's method is the most widespread high-order method, demanding the gradient and the Hessian of the objective function. However, one of the main disadvantages of Newtons method is its lack of global convergence and high iteration cost.…
Generalized Nash equilibrium (GNE) is a solution concept for complete information games, in which each player's objective function and feasible region depend on other players' actions. While numerical methods for finding GNE when players…
This paper studies the problem of robustly optimal operation control of microgrids with a high share of renewable energy sources. The main goal is to ensure optimal operation under a wide range of circumstances, given the highly…
We introduce Pattern-based Kernel Search (PaKS), a two-phase matheuristic for the solution of the Single-Source Capacitated Facility Location Problem (SSCFLP). In the first phase, PaKS employs a pattern recognition technique to identify an…
This paper presents a concise overview of sensitivity-based methods for solving large-scale optimization problems in distributed fashion. The approach relies on sensitivities and primal decomposition to achieve coordination between the…
We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of…
This paper applies computational techniques of convex stochastic optimization to optimal operation and valuation of electricity storages in the face of uncertain electricity prices. Our valuations are based on the indifference pricing…
This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimization), a new hierarchy of semidefinite programming…
Integrating data-driven techniques with mechanism-driven insights has recently gained popularity as a powerful learning approach to solving traditional LQR problems for designing intelligent controllers in complex dynamic systems. However,…
Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other…