最优化与控制

A number of important modern applications in optimal control can be formulated as open loop control problems in which the underlying dynamical systems are subject to random inputs. These so-called ensemble control problems require the…

Identifiability means that iterates generated by optimization algorithms are eventually confined to an identifiable set. This property is computationally useful because minimizing a nonsmooth function near a critical point reduces to…

We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically. We show that the resulting method, per-sample clipped SGD (PS-Clip-SGD), achieves optimal…

We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…

We study optimal decision policies for integer linear programs with a fixed feasible set and varying cost vectors, represented as linear decision trees. Once synthesized for a given feasible set, they return an optimal solution for any…

We obtain an explicit solution for the static Kullback--Leibler (KL) unbalanced optimal transport problem between finite non-degenerate Gaussian measures with quadratic cost, two independent positive marginal relaxation parameters, and no…

We study the maximum $k$-colorable subgraph (M$k$CS) problem, which consists in finding a largest $k$-colorable induced subgraph in a given graph. We consider a Semidefinite Programming (SDP) relaxation for the M$k$CS problem and regard its…

Regenerating braking energy is one major pathway to make rail traffic energy-efficient. It is therefore desirable to design timetables that exploit this feature. However, timetables that allow to regenerate energy are often bad for the…

The rapid proliferation of omnichannel retail strategies has fundamentally transformed store replenishment operations in uncertain supply chain environments. With retail stores increasingly acting as hybrid fulfillment centers, pooled…

Minimum distance constraints (minDCs) appear in many geometric optimization problems. They pose major challenges for mixed-integer nonlinear programming (MINLP) due to their reverse-convexity. We develop new algorithms for tightening…

In this work, we reveal a rich combinatorial structure underlying exact minimax optimal algorithms for classical nonexpansive fixed-point problems. This viewpoint unifies all extremal optimal methods and provides a systematic and practical…

We introduce PF-AGD, the first parameter-free, deterministic, accelerated first-order method to achieve $O(\epsilon^{-5/3}\log(1/\epsilon))$ oracle complexity bound when minimizing sufficiently smooth, non-convex functions; this is the…

In this work we consider the multi-agent motion planning (MAMP) problem with the constraint that agents arrive at their respective goals at the same time. For the special case where all agents are initially at rest we propose a two-step…

We study a decentralized linear quadratic Gaussian control problem, in which a leader and a follower must steer a linear system to a target state. The target state is known only to the leader, and no explicit communication channel exists…

We consider constrained linear-quadratic dynamic games arising in autonomous vehicle platooning, intersection crossing and other cooperative driving scenarios. Infinite-horizon Nash equilibria are reformulated as receding-horizon affine…

We consider an optimal transport problem between laws of random probability measures: given a base cost function, we build the associated OT cost between probability measures that in turn we use to define the OT cost between probability…

Bilevel learning refers to machine learning problems that can be formulated as bilevel optimization models, where decisions are organized in a hierarchical structure. This paradigm has recently gained considerable attention in machine…

Motivated by previous efforts toward mathematically analyzing the treatment of monomials in spatial branch-and-bound, we study the convex hull of the graph of a simple monomial on a nonnegative box domain in arbitrary dimension, where at…

In this study, we identify a class of redundant transitivity constraints in a 0-1 integer linear programming formulation of the clique partitioning problem. The transitivity constraints in this class can be removed from the formulation…

Tensor completion has emerged as a powerful framework for recovering missing data in multidimensional signals by exploiting low-rank tensor structures. Among existing approaches, linear transform-based tensor nuclear norm (TNN) methods have…