337 papers
This paper extends the Edge of Stability phenomenon to non-Euclidean gradient descent by introducing a generalized sharpness measure based on directional smoothness, demonstrating that diverse optimizers exhibit similar stability thresholds and oscillatory behaviors across arbitrary geometric norms.
This paper presents a formal control synthesis framework for continuous-state stochastic systems that minimizes a linear combination of system entropy (measured by KL divergence to uniform) and cumulative cost by deriving novel bounds on the entropy difference between continuous distributions and their finite-state abstractions, thereby enabling entropy-aware controllers with rigorous performance guarantees.
This paper extends the homogeneous second-order descent method (HSODM) to bound-constrained nonlinear optimization by proposing the SOBASIP algorithm, which utilizes affine scaling and homogenization techniques to achieve a global iteration complexity of for finding -approximate second-order stationary points and exhibits local superlinear convergence.
This paper proposes a computationally efficient, robust adaptive nonlinear model predictive control algorithm that utilizes ellipsoidal tubes to guarantee constraint satisfaction and stability for learning-based systems with unknown parameters and set-bounded disturbances.
This paper establishes the boundary stabilization of flows in star-shaped and tree-shaped open channel networks governed by Saint-Venant equations with friction by constructing a novel explicit Lyapunov function that enables optimal control using only terminal node actuators, even in the absence of internal controls.
This paper addresses a strong NP-hard bilevel optimistic scheduling problem on uniform parallel machines, where a leader minimizes weighted tardy jobs and a follower minimizes total completion time, by establishing its complexity via reduction from Numerical 3-Dimensional Matching and proposing exact solution methods including a dynamic programming algorithm, a MIP formulation, and a branch-and-bound approach with column generation that effectively solve instances up to 80 jobs and 4 machines.
This paper investigates optimization problems constrained by parametric variational inequalities on moving sets by establishing the Lipschitz continuity of the solution function and automatic metric regularity, and proposes a Smoothing Implicit Gradient Algorithm (SIGA) that is proven to converge to a stationary point and validated through real-world portfolio management applications.
This paper presents methods to compute the Scaled Relative Graph (SRG) of discrete-time linear-time-invariant systems exactly from state-space models and exclusively from input-output data, while also introducing a robust SRG formulation capable of handling noisy trajectories.
This paper establishes a unified bounded-variation solution framework for prox-regular sweeping processes by proving the equivalence between a new integral formulation with a quadratic correction term and the standard differential-measure formulation, while also deriving a Brézis-Ekeland-Nayroles-type variational characterization that ensures stability under uniform limits.
This paper introduces convex optimization, specifically Linear Programming, as a tool to solve the inverse micromechanics problem for isotropic composites with spherical inclusions by determining component volume fractions from known dielectric constants and effective properties using the Eshelby-Mori-Tanaka model.
This paper resolves two major open problems by proving that computing shortest monotone paths on simple polytopes and determining their diameters are NP-hard, while also demonstrating that polynomial-time linear paths can be found on specific small extended formulations of any polytope.
This paper proposes a novel three-stage framework that combines inexpensive imperfect labels, supervised pretraining, and self-supervised refinement to achieve effective amortized optimization with significantly reduced costs and improved performance across challenging domains.
This paper introduces an adaptive multilevel Newton-type method that automatically switches to full Newton steps once quadratic convergence is achievable, thereby overcoming the initial slow convergence of standard Newton methods while consistently outperforming both first-order and classical multilevel approaches on strongly convex and self-concordant functions.
This paper extends tracking guarantees for time-varying variational inequalities to non-monotone functions and periodic problems without sublinear solution paths, while also demonstrating that the associated discrete dynamical systems can exhibit either convergence or provably chaotic behavior.
This paper establishes a superposition theorem for input-to-output stability in a broad class of nonlinear infinite-dimensional systems by introducing novel stability concepts and criteria, while also addressing the specific challenges of extending such results from finite-dimensional and state-based frameworks through counterexamples.
This research presents a robust dual-layer network flow model for semiconductor wafer supply chains that effectively addresses stochastic batch transfers and logistical bottlenecks, resulting in significant improvements in cost efficiency, productivity, resource utilization, and capacity.
This paper presents a real-time, optimization-based human-in-the-loop energy and thermal management system for electric racing cars that utilizes a tunable lift-off-throttle signal and adaptive feedback control to achieve near-optimal stint performance while respecting energy and thermal constraints.
This paper proposes a novel Linear Parameter-Varying (LPV) framework utilizing Integral Quadratic Constraints (IQCs) to analyze and establish quantitative tracking error bounds for iterative first-order optimization algorithms applied to time-varying convex problems, where the bounds depend on specific measures of temporal variability such as function value and gradient rates of change.
This paper investigates generalized -support dual norms derived from arbitrary source norms to enforce a strict -sparsity budget, establishing conditions for their effectiveness through the analysis of exposed faces and revealing that their unit ball faces are structurally hypersimplices when the source norm is an -norm.
This paper introduces the Morse parametric qualification condition to establish a relevant intermediate class for bilevel programming and analyzes two gradient-based solution strategies: a biased single-step multi-step method with rich theoretical properties and a simpler, though less stable, differentiable programming approach.