最优化与控制

We present a dynamical version for the multi-marginal optimal transport problem with infimal convolution cost, using the theory of Wasserstein barycentres. We show, how our formulation relates to the dynamical version of the multi-marginal…

Consider the problem of finding a zero of a finite sum of maximally monotone operators, where some operators are Lipschitz continuous and the rest are potentially set-valued. We propose a forward-backward-type algorithm for this problem…

This thesis investigates the design of algorithms for solving min-max optimization problems, which form the mathematical foundation of many modern applications in machine learning, game theory, and optimization. This work offers new…

Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…

Deep learning approaches, known for their ability to model complex relationships and fast execution, are increasingly being applied to solve large optimization problems. However, existing methods often face challenges in simultaneously…

We study the polynomial optimization problem of minimizing a multihomogeneous polynomial over the product of spheres. This polynomial optimization problem models the tensor optimization problem of finding the best rank one approximation of…

Nonlinear inverse problems pervade engineering and science, yet noisy, non-differentiable, or expensive residual evaluations routinely defeat Jacobian-based solvers. Derivative-free alternatives either demand smoothness, require large…

Stochastic convex optimization problems with nonlinear functional constraints are ubiquitous in signal processing applications including constrained least-squares, set-membership adaptive filtering, and trajectory optimization under…

We study distributed optimization of finite-degree polynomial Laplacian spectral objectives under fixed topology and a global weight budget, targeting the collective behavior of the entire spectrum rather than a few extremal eigenvalues. By…

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

We formulate and solve the fixed horizon linear quadratic covariance steering problem in continuous time with a terminal cost measured in Hilbert-Schmidt (i.e., Frobenius) norm error between the desired and the controlled terminal…

We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…

In this article, we tackle the problem of the existence of a gap corresponding to Young measure relaxations for state-constrained optimal control problems. We provide a counterexample proving that a gap may occur in a very regular setting,…

This paper presents a hybrid optimization methodology for parameter estimation of reactive transport systems. Using reduced-order advection-diffusion-reaction (ADR) models, the computational requirements of global optimization with dynamic…

We propose and study a variant of the Dai-Liao spectral conjugate gradient method, developed through an analysis of eigenvalues and inspired by a modified secant condition. We show that our proposed method is globally convergent for general…

Frank-Wolfe (FW) algorithms have emerged as an essential class of methods for constrained optimization, especially on large-scale problems. In this paper, we summarize the algorithmic design choices and progress made in the last years of…

We consider the (sub-Riemannian type) control problem of finding a path going from an initial point $x$ to a target point $y$, by only moving in certain admissible directions. We assume that the corresponding vector fields satisfy the…

We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength, both in a weighted…

SeDuMi and SDPT3 are two solvers for solving Semi-definite Programming (SDP) or Linear Matrix Inequality (LMI) problems. A computational performance comparison of these two are undertaken in this paper regarding the Stability of…

In recent years, there has been a surge of machine learning applications developed with hierarchical structure, which can be approached from Bi-Level Optimization (BLO) perspective. However, most existing gradient-based methods overlook the…