最优化与控制

This work proposes a framework, embedded within the Performance Estimation framework (PEP), for obtaining worst-case performance guarantees on stochastic first-order methods. Given a first-order method, a function class, and a noise model…

In this paper, we investigate the problem of differentially private distributed optimization. Recognizing that lower sensitivity leads to higher accuracy, we analyze the key factors influencing the sensitivity of differentially private…

In this paper, we propose a systematic approach for extending first-order optimization algorithms, originally designed for unconstrained strongly convex problems, to handle closed and convex set constraints. We show that the resulting…

We formulate a Contract for Difference (CfD) with early exit options as a two-player zero-sum Dynkin game, reflecting the strategic interaction between an electricity producer and a regulatory entity. The game incorporates penalties for…

The entropic risk measure is widely used in high-stakes decision-making across economics, management science, finance, and safety-critical control systems because it captures tail risks associated with uncertain losses. However, when data…

This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these…

We propose a new first-order method for minimizing nonconvex functions with Lipschitz continuous gradients and H\"older continuous Hessians. The proposed algorithm is a heavy-ball method equipped with two particular restart mechanisms. It…

Multi-objective optimization studies the process of seeking multiple competing desiderata in some operation. Solution techniques highlight marginal tradeoffs associated with weighing one objective over others. In this paper, we consider…

Minimizing the sum of a convex function and a composite function appears in various fields. The generalized Levenberg--Marquardt (LM) method, also known as the prox-linear method, has been developed for such optimization problems. The…

Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and…

We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…

Optimal control provides a principled framework for transforming dynamical system models into intelligent decision-making, yet classical computational approaches are often too expensive for real-time deployment in dynamic or uncertain…

Passive and bistatic radar systems are often limited by strong clutter and direct-path interference that mask weak moving targets. Conventional cancellation methods such as the extensive cancellation algorithm require careful tuning and can…

In this paper, we propose an efficient numerical approach for solving a specific type of quartic inhomogeneous polynomial optimization problem inspired by practical applications. The primary contribution of this work lies in establishing an…

We study constant-factor approximation algorithms for the Bin Packing Problem with Setups (BPPS). First, we show that adaptations of classical BPP heuristics can have arbitrarily poor worst-case performance on BPPS instances. Then, we…

Risk management often plays an important role in decision making under uncertainty. In quantitative risk management, assessing and optimizing risk metrics requires efficient computing techniques and reliable theoretical guarantees. In this…

In this paper, we consider a class of constrained multiobjective optimization problems, where each objective function can be expressed by adding a possibly nonsmooth nonconvex function and a differentiable function with Lipschitz continuous…

In this paper, we investigate the existence and characterization of the value for a two-player zero-sum differential game with symmetric incomplete information on a continuum of initial positions and with signal revelation. Before the game…

This technical report presents a comprehensive study of SDPT3, a widely used open-source MATLAB solver for semidefinite-quadratic-linear programming, which is based on the interior-point method. It includes a self-contained and consistent…

We introduce a general probabilistic framework for discrete-time, infinite-horizon discounted Mean Field Type Games (MFTGs) with both global common noise and team-specific common noises. In our model, agents are allowed to use randomized…