最优化与控制
The Whittle index for restless bandits (two-action semi-Markov decision processes) provides an intuitively appealing optimal policy for controlling a single generic project that can be active (engaged) or passive (rested) at each decision…
We propose a stochastic trust-region method for unconstrained nonconvex optimization that incorporates stochastic variance-reduced gradients (SVRG) to accelerate convergence. Unlike classical trust-region methods, the proposed algorithm…
We study an online linear programming (OLP) model in which inventory is not provided upfront but instead arrives gradually through an exogenous stochastic replenishment process. This replenishment-based formulation captures operational…
This paper presents a static event-triggered control strategy for multivariable Newton-based extremum seeking. The proposed method integrates event-triggered actuation into the Newton-based optimization framework to reduce control updates…
In this article, we formulate topology optimization problems concerning the mass distribution as minimization problems for functionals on the Wasserstein space. We relax optimization problems regarding non-convex objective functions on the…
We study the subgradient method for factorized robust signal recovery problems, including robust PCA, robust phase retrieval, and robust matrix sensing. The resulting objectives are nonsmooth and nonconvex, and can have unbounded sublevel…
We study the generalized forward-reflected-backward (GFRB) method, an extension of the forward-reflected-backward (FRB) scheme due to Malitsky and Tam, for solving monotone inclusion problems in real Hilbert spaces. We first analyze GFRB…
The Polyak stepsize has been proven to be a fundamental stepsize in convex optimization, giving near optimal gradient descent rates across a wide range of assumptions. The universality of the Polyak stepsize has also inspired many…
Low-rank matrix recovery is well-known to exhibit benign nonconvexity under the restricted isometry property (RIP): every second-order critical point is globally optimal, so local methods provably recover the ground truth. Motivated by the…
Effective risk monitoring in dynamic environments such as disaster zones requires an adaptive exploration strategy to detect hidden threats. We propose a bi-level unmanned aerial vehicle (UAV) monitoring strategy that efficiently integrates…
Sample average approximation (SAA) is a technique for obtaining approximate solutions to stochastic programs that uses the average from a random sample to approximate the expected value that is being optimized. Since the outcome from…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
Unit Commitment (UC) and Optimal Power Flow (OPF) are two fundamental problems in short-term electric power systems planning that are traditionally solved sequentially. The state-of-the-art mostly uses a direct current flow approximation of…
In this paper, we study a delayed forward-backward stochastic control system in which all the coefficients depend on the state and control terms, and the control domain is not necessarily convex. A global stochastic maximum principle is…
In this paper we develop a Bregman regularized proximal point algorithm for solving monotone equilibrium problems on Hadamard manifolds. It has been shown that the regularization term induced by a Bregman function is, in general, nonconvex…
Barn-type houses have become one of the most popular single-family housing typologies in Poland and across Europe due to their simplicity, functionality, and potential for energy efficiency. Despite their widespread use, systematic methods…
In this paper, we develop a rigorous mathematical framework for the optimization of hip roof house geometry, with the primary goal of minimizing the external surface of the building envelope for a given set of design constraints. Five…
The geometric form of a building strongly influences its material use, heat losses, and energy efficiency. This paper presents an analytical optimization of L-shaped residential buildings aimed at minimizing the external surface area for a…
We consider a constrained eigenvalue optimization problem that arises in an important nonlinear dynamical model for mRNA translation in the cell. We prove that the ordered list of optimal parameters admits a turnpike property, namely, it…
The inherent non-convexity of poriferous surfaces typically entraps agents in local minima and complicates workload distribution. To resolve this, we propose a distributed diffeomorphic coverage control framework for the multi-agent system…