最优化与控制
We consider the densest submatrix problem, which seeks the submatrix of fixed size of a given binary matrix that contains the most nonzero entries. This problem is a natural generalization of fundamental problems in combinatorial…
This paper develops a reinforcement learning-based controller for the stabilization of partial differential equation (PDE) systems. Within the soft actor-critic (SAC) framework, we embed a DeepONet, a well-known neural operator (NO), which…
We consider a class of nonconvex nonsmooth multicomposite optimization problems where the objective function consists of a Tikhonov regularizer and a composition of multiple nonconvex nonsmooth component functions. Such optimization…
We consider unconstrained multi-criteria optimization problems with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust region framework where additional sampling approach is used to govern the sample size…
We observe that the diameter of small (in a locally uniform sense) balls in $C^{1,1}$ sub-Riemannian manifolds equals twice the radius. We also prove that, when the regularity of the structure is further lowered to $C^0$, the diameter is…
In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…
This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…
In this work, we address unconstrained finite-sum optimization problems, with particular focus on instances originating in large scale deep learning scenarios. Our main interest lies in the exploration of the relationship between recent…
This work tackles a class of optimization problems in which fixing some well-chosen combinations of the variables makes the problem substantially easier to solve. We consider that the variables space may be partitioned into subsets that fix…
This paper considers the problem of minimizing a differentiable function with locally Lipschitz continuous gradient on the algebraic variety of real matrices of upper-bounded rank. This problem is known to enable the formulation of various…
Most data-driven analysis and control methods rely on centralized access to system measurements. In contrast, we consider a setting in which the measurements are distributed across multiple agents and raw data are not shared. Each agent has…
Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…
Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence. When deployed on low-precision hardware, weights are…
This paper establishes a general topological condition under which the semilocal stability of a set-valued mapping can be exactly determined by its local stability properties. Specifically, we investigate the relationship between the…
Mean field games (MFGs) model the limit of large populations of strategically interacting agents, yet both forward and inverse problems remain challenging. For the forward problem, a difficulty is to design numerical methods with global…
A banded matrix is a real square matrix where nonzero entries appear around the main diagonal. In this article, we consider linear complementarity properties of (variants) of banded matrices. Focusing on triangular matrices and the newly…
Conventional stochastic control methods have several limitations. They focus on optimizing the average performance and, in some cases, performance variability; however, their problem settings still require an explicit specification of the…
In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality…
We establish Hoeffding-type concentration inequalities for the low and high tail bounds of sums of exchangeable random variables. Our results exhibit an anti-symmetry in such tail bounds due to the assumption of exchangeability, a…
In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg…