295 papers
This paper investigates linear-quadratic Dirichlet control problems governed by non-coercive elliptic equations on non-convex polygonal domains using energy regularization, establishing solution regularity in weighted Sobolev spaces and deriving optimal error estimates for finite element discretizations that employ graded meshes and a specialized discrete projection.
This paper presents an integer linear programming model to formalize the rules of the Nikoli puzzle Evolomino and introduces an algorithm for generating unique instances, demonstrating that state-of-the-art solvers can efficiently solve grids up to 18x18.
This paper introduces mollified Christoffel-Darboux kernels on algebraic varieties to achieve a uniform boundedness property on the support and enable consistent, quantitatively controlled density recovery from moment data without prior knowledge of the equilibrium measure.
This paper proposes a stochastic alternating direction method of multipliers (ADMM) for nonsmooth composite convex optimization in Hilbert spaces, proving its strong convergence and establishing faster nonergodic convergence rates for both strongly and general convex cases, with applications demonstrated in PDE-constrained problems with random coefficients.
This paper proposes a categorical framework for convex optimization by defining a category where optimization problems are objects, utilizing this structure to rederive key results such as a minimax-type theorem and the involution property of the Legendre dual.
This paper proposes and analyzes a finite-horizon approximation method for computing feedback Nash equilibria in infinite-horizon discrete-time linear-quadratic games, establishing conditions for equilibrium uniqueness, providing an efficient solution algorithm, and proving the convergence of costs with explicit error bounds.
This paper introduces Filtered Control Barrier Functions (FCBFs), a framework that integrates an input regularization filter with High-Order CBFs within a unified quadratic program to simultaneously guarantee system safety, control bounds, and Lipschitz continuity of control inputs, thereby preventing abrupt changes that could degrade performance or violate actuator limits.
This paper proposes a robust control and gain scheduling approach that mitigates distributional shifts in approximant model parameters caused by system nonlinearity by constraining the closed-loop system to remain consistent with learning data, a problem formulated as a computationally efficient convex semi-definite program.
This paper introduces SHANG and SHANG++, two accelerated stochastic gradient descent methods derived from Hessian-driven Nesterov flows that achieve robust convergence and superior performance under multiplicative noise scaling, with SHANG++ specifically demonstrating near-optimal accuracy in deep learning applications even in high-noise environments.
This paper demonstrates the successful real-time deployment of a dual active-set solver (DAQP) for high-frequency (500 Hz) Model Predictive Control on a resource-constrained nano-quadcopter, showing superior execution times compared to ADMM-based methods and introducing a data-driven approach to certify real-time feasibility offline.
This paper proposes a novel, efficient three-stage closed-form solution for robust adaptive beamforming that outperforms existing benchmarks like MOSEK and RMVB in computational speed, handles rank-deficient covariance scenarios, and establishes previously unstudied existence and uniqueness conditions.
This paper analyzes a two-stage queueing system in telehealth settings to derive structural insights for optimal decision-making by nurse practitioners, ultimately proposing robust, near-optimal heuristics that effectively balance service quality and wait times while offering actionable guidance on telemedicine infrastructure investments.
This paper proposes the RE-RPfair model, an extension of the Renewable Energy Robust Optimization Problem, which incorporates the Gini Index to ensure fair allocation of renewable energy suppression among PV sources while addressing uncertainties in unit commitment.
This paper proposes DPS-LA, a novel distributed optimization algorithm that overcomes the dependency on unknown global optimal values by using level-value adjustments and linear feasibility problems to achieve parameter-free adaptability, network consensus, and a linear speedup convergence rate of .
This paper analyzes the solvability of parameter estimation-based observers (PEBO) for general nonlinear systems by examining the fundamental properties of transformability and identifiability, ultimately providing sufficient conditions to ensure their existence.
This paper establishes that for positive recurrent Lévy diffusions driven by scaled Brownian motion and -stable processes ($1<\alpha<2$) in the small noise regime, the large-time limiting behavior of the one-dimensional marginal distribution is determined by the optimal value of a deterministic control problem featuring both continuous and impulse controls.
This paper introduces a method for computing less conservative -gain bounds for nonlinear Lur'e systems over restricted frequency and amplitude ranges by combining Scaled Relative Graphs with Sobolev theory, resulting in a three-dimensional nonlinear generalization of the Bode diagram that recovers both the standard LTI Bode plot and the global -gain as limiting cases.
This paper investigates Max-Cut instances on complete graphs with geometrically decreasing edge weights, establishing a sharp phase diagram for the optimality of isolated cuts based on threshold polynomials and conjecturing their global optimality for sufficiently large .
This paper characterizes the approximate Nash equilibrium of competing decentralized exchanges setting dynamic fees, revealing that while the two-regime fee structure persists, competition shifts the fee-switching boundary to a weighted average of oracle and competitor rates, ultimately reducing slippage for strategic traders while having activity-dependent effects on noise traders.
This paper proposes a column-generation-based algorithmic framework to efficiently solve both splittable and unsplittable variants of the capacitated Multi-Commodity Flow problem with convex, potentially non-differentiable, link cost functions, offering a robust optimization approach for managing traffic in telecommunication networks.