最优化与控制

This paper is devoted to the analysis of periodic solutions of nonlinear control-affine systems with bang-bang controls. Such problems naturally arise in periodic optimal control with constrained inputs, which have, in particular, important…

We study the problem of learning the input-output map of a controlled vibrating plate with a composite structure from experimental measurements. Analytical modeling of this control system faces challenges due to the essential orthotropy and…

We present a \emph{mirror-free} mirror prox (MFMP) algorithm, which extends the classic approach of Nemirovski (2004) to allow for proximal-like updates without the explicit need for a mirror map. We further analyze the convergence of our…

We propose a mathematical framework to explain implicit regularization from early stopping during the training of overparametrized neural networks. In the mean-field limit, the parameter distribution evolves according to a gradient flow on…

The paper addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a…

In this work, we propose derivative-free framework for bilevel optimization. We consider both the upper and lower-level problems with bound constraints on the variables, as well as general nonlinear constraints, assuming that first-order…

In this paper, we study the local convergence of the standard ADMM scheme for a class of nonconvex composite problems arising from modern imaging and machine learning models. This problem is constrained by a closed convex set, while its…

We consider a realistic decentralized setup with bandwidth-constrained communication and derive optimal time complexities for non-convex stochastic parallel and asynchronous optimization (up to logarithmic factors). We develop the…

In this paper, we propose a a gradient-based neural network model to solve the mathematical programming problems with complementary constraints (MPCC). In order to facilitate tractable optimization, the problem MPCC is transformed via a…

There is a growing literature adopting a stochastic optimal control (SOC) perspective to fine-tune diffusion models and related generative policies. A prominent class of methods, known as iterative diffusion optimization, solves the SOC…

We study the relationship between disturbance decoupling (DD) and H2 optimal control for linear time-invariant (LTI) systems, revealing a fundamental gap between DD subspace constraints and semi-definite program (SDP)-based H2 minimization.…

The number of electric vehicles is rapidly increasing worldwide. This growth brings significant environmental benefits but also introduces new challenges: uncoordinated charging can place stress on the grid, particularly during peak hours.…

We develop a finite-data framework for certifying \emph{zero-defect} (neutral) configurations of positive vectors under the canonical separable reciprocal cost. We show that this scalar cost is characterized among non-constant continuous…

In this paper, we evaluate stochastic-computing simulated annealing (SC-SA) for solving large-scale combinatorial optimization problems. SC-SA is designed using stochastic computing, where the computatoin is reazlied using random bitstream,…

This paper proposes the first fully distributed algorithm for finding the Generalized Nash Equilibrium (GNE) of a non-cooperative game with shared coupling constraints and general cost coupling at a user-prescribed finite time T. As a…

We study a stochastic anchored gradient scheme, namely HalpernSGD, which combines the classical Halpern iteration for finding a minimizer of a convex and $L$-smooth objective function with a stochastic {first-order} oracle. The algorithm is…

The Krasnoselskii-Mann iteration is an important algorithm in optimization and variational analysis for finding fixed points of nonexpansive mappings. In the general case, it produces a sequence converging \emph{weakly} to a fixed point…

We propose a mathematical model for the growth and treatment dynamics of Undifferentiated Pleomorphic Sarcoma (UPS) based on a system of nonlinear differential equations. The model integrates Gompertz-type tumor growth with surface-area…

The Krasnosel'ski\u{\i}--Mann and Halpern iterations are classical schemes for approximating fixed points of nonexpansive mappings in Banach spaces, and have been widely studied in more general frameworks such as $CAT(\kappa)$ and, more…

Electricity distribution companies deploy battery storage to defer grid upgrades by reducing peak demand. In deregulated jurisdictions, such storage often sits idle because regulatory constraints bar participation in electricity markets.…