最优化与控制
New approaches to the theory of dynamic programming view dynamic programs as families of policy operators acting on partially ordered sets. In this paper, we extend these ideas by shifting from arbitrary partially ordered sets to ordered…
In this paper, we investigate how structural properties of the constraint system impact the oracle complexity of smooth non-convex optimization problems with convex inequality constraints over a simple polytope. In particular, we show that,…
This paper develops an analytical strategy for solving the linear quadratic pursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the pursuer and evader is described using the controlled Tschauner-Hempel equations, and…
The continuous-time analysis of existing iterative algorithms for optimization has a long history. This work proposes a novel continuous-time control-theoretic framework for equality-constrained optimization. The key idea is to design a…
We consider the problem of optimising the expected value of a loss functional over a nonlinear model class of functions, assuming that we have only access to realisations of the gradient of the loss. This is a classical task in statistics,…
In the present paper, we formulate two versions of Frank--Wolfe algorithm or conditional gradient method to solve the DC optimization problem with an adaptive step size. The DC objective function consists of two components; the first is…
In this contribution, the optimal stabilization problem of periodic orbits is studied via invariant manifold theory and symplectic geometry. The stable manifold theory for the optimal point stabilization case is generalized to the case of…
Cardinal Optimizer is a high-performance mathematical programming solver for efficiently solving largescale optimization problem. This documentation provides basic introduction to the Cardinal Optimizer.
Voltage (Volt) and reactive-power (VAR) control in transmission networks is critical for reliability and increasingly needs fast, implementable decisions. This paper presents a transmission Volt/VAR Optimization (VVO) framework that…
Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelerating standard fixed-point iteration schemes provides a…
We present a batched first-order method for solving multiple linear programs in parallel on GPUs. Our approach extends the primal-dual hybrid gradient algorithm to efficiently solve batches of related linear programming problems that arise…
We show that computing even very coarse approximations of critical points is intractable for simple classes of nonconvex functions. More concretely, we prove that if there exists a polynomial-time algorithm that takes as input a polynomial…
Matching platforms, from ridesharing to food delivery to competitive gaming, face a fundamental operational dilemma: match agents immediately to minimize waiting costs, or delay to exploit the efficiency gains of thicker markets. Yet…
Bilevel optimization problems consist of minimizing a value function whose evaluation depends on the solution of an inner optimization problem. These problems are typically tackled using first-order methods that require computing the…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional. It involves BSDEs in $L^1$ whose well-posedness is a subtle issue. A suitable framework has been adopted so that…
Diagonalizability plays an important role in the analysis and design of multivariable systems. A structured matrix is called structurally diagonalizable if almost all of its numerical realizations, obtained by assigning real values to its…
This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model…
Norm-constrained linear minimization oracle (LMO)-based optimizers such as spectral gradient descent and Muon are attractive in large-scale learning, but extending them to manifold-constrained problems is nontrivial and often leads to…
This paper aims to accelerate decentralized optimization by strategically designing the edge weights used in the agent-to-agent message exchanges. We propose a Dynamic Directed Decentralized Gradient (D3GD) framework and show that the…
Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…