332 papers
The paper proposes Deep FlexQP, a deep unfolding-based solver that accelerates nonlinear programming by learning dimension-agnostic parameters for a robust, always-feasible convex QP relaxation, thereby significantly improving the speed and success rates of SQP and safety filter applications while providing rigorous performance guarantees.
This paper proposes D-APDB, a distributed accelerated primal-dual algorithm with backtracking that achieves optimal convergence for decentralized constrained optimization over undirected networks without requiring prior knowledge of Lipschitz constants, making it the first method of its kind to handle private nonlinear constraints efficiently.
This paper establishes sharper convergence guarantees for the Muon optimizer by providing a direct, simplified analysis that achieves faster convergence rates under broader problem settings than existing restrictive theoretical frameworks.
This paper proposes a variational framework that interprets transformer layers as optimization iterations, enabling the design of a Nesterov-accelerated transformer architecture that outperforms standard baselines on language modeling tasks.
This paper demonstrates that the robust permutation flowshop problem under budgeted uncertainty can be solved by reducing it to polynomially many nominal instances, thereby establishing polynomial-time solvability for two machines and polynomial-time approximability for any fixed number of machines.
This paper establishes that the real image of a G-invariant variety is metrically rare within its quotient space, a geometric property that explains the prevalence of symmetry in optimization problems by showing that critical points and global minima are statistically driven toward high-symmetry boundary strata.
This paper proposes a rare event-aware control method for power systems that utilizes a Fleming-Viot particle approach within a multistage stochastic programming framework to generate biased scenarios of prolonged renewable energy shortfalls, thereby enabling cost-effective and robust ramping of conventional power plants.
This paper establishes that mixed H2/H-infinity control exhibits benign nonconvexity where every stationary point is globally optimal, by characterizing the feasible set's topology and employing an Extended Convex Lifting framework to bridge nonconvex policy optimization with convex reformulations for scalable, data-driven applications.
This paper addresses the problem of set-membership localization using noisy range measurements by characterizing the nonconvex set of consistent points and developing efficient convex programming methods to compute tight, guaranteed outer-bounding boxes or ellipsoids, as well as inner approximations, without relying on semidefinite programming relaxations.
This paper presents a probabilistic solution for linear-quadratic optimal control problems with state constraints, providing a representation for the value function and an explicit optimal control that keeps the system within a specified domain while minimizing quadratic control costs.
This paper demonstrates that for high-dimensional random data, gradient descent on shallow ReLU networks exhibits an implicit bias that approximates the minimum -norm solution with high probability, bridging the gap between worst-case non-existence and exact orthogonality results through a novel primal-dual analysis.
This paper introduces the double Zarankiewicz number , defined via bipartite graphs allowing "double edges" corresponding to squared bilinear forms, to establish improved lower bounds for the maximum SOS rank of biquadratic forms and resolve the previously noted gap in the $4\times3$ case.
This paper introduces U-OBCA, an uncertainty-aware optimization-based collision avoidance framework that utilizes Wasserstein distributionally robust chance constraints to handle polygon-shaped robots and obstacles without geometric simplification, thereby significantly reducing conservatism and improving navigation efficiency in narrow, cluttered environments compared to existing methods.
This paper proposes the NSGDA-M algorithm, a stochastic first-order method with momentum and normalization, to solve nonconvex-strongly concave minimax problems under generalized smoothness conditions, achieving an stochastic gradient complexity for finding an -stationary point.
This paper introduces a computationally tractable framework for stochastic optimal control in partially observable, nonlinear systems that explicitly integrates feedforward planning with feedback uncertainties, demonstrating how muscle co-contraction in human neuromechanics emerges as an optimal adaptation to sensorimotor constraints.
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.