Related papers: Explicit continuation methods with L-BFGS updating…
Linear systems in applications are typically well-posed, and yet the coefficient matrices may be nearly singular in that the condition number $\kappa(\boldsymbol{A})$ may be close to $1/\varepsilon_{w}$, where $\varepsilon_{w}$ denotes the…
Post-training quantization (PTQ) of large language models (LLMs) to extremely low bit-widths remains challenging due to the fundamental trade-off between computational efficiency and representational capacity. While existing ultra-low-bit…
Motivated by the potential for parallel implementation of batch-based algorithms and the accelerated convergence achievable with approximated second order information a limited memory version of the BFGS algorithm has been receiving…
Successive quadratic approximations, or second-order proximal methods, are useful for minimizing functions that are a sum of a smooth part and a convex, possibly nonsmooth part that promotes regularization. Most analyses of iteration…
We propose and analyze an extended Fourier pseudospectral (eFP) method for the spatial discretization of the Gross-Pitaevskii equation (GPE) with low regularity potential by treating the potential in an extended window for its discrete…
This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not…
We present the barycentric Lagrange dual tree traversal (BLDTT) fast summation method for particle interactions. The scheme replaces well-separated particle-particle interactions by adaptively chosen particle-cluster, cluster-particle, and…
Solving real-time quadratic programming (QP) is a ubiquitous task in control engineering, such as in model predictive control and control barrier function-based QP. In such real-time scenarios, certifying that the employed QP algorithm can…
In this paper, we propose a trust-region interior-point stochastic sequential quadratic programming (TR-IP-SSQP) method for solving optimization problems with a stochastic objective and deterministic nonlinear equality and inequality…
Long-term location tracking, where trajectory compression is commonly used, has gained high interest for many applications in transport, ecology, and wearable computing. However, state-of-the-art compression methods involve high space-time…
LLMs demonstrate strong performance in auto-mated software engineering, particularly for code generation and issue resolution. While proprietary models like GPT-4o achieve high benchmarks scores on SWE-bench, their API dependence, cost, and…
In this paper, we present an equivalent convex optimization formulation for discrete-time stochastic linear systems subject to linear chance constraints, alongside a tight convex relaxation for quadratic chance constraints. By lifting the…
This paper considers optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function, and proposes stochastic composite proximal bundle (SCPB) methods for solving it.…
Large Language Models (LLMs) exhibit remarkable proficiency in addressing a diverse array of tasks within the Natural Language Processing (NLP) domain, with various prompt design strategies significantly augmenting their capabilities.…
This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…
We propose a novel application of coded computing to the problem of the nearest neighbor estimation using MatDot Codes [Fahim. et.al. 2017], that are known to be optimal for matrix multiplication in terms of recovery threshold under storage…
We investigate fast direct methods for solving systems of the form (B + G)x = y, where B is a limited-memory BFGS matrix and G is a symmetric positive-definite matrix. These systems, which we refer to as shifted L-BFGS systems, arise in…
In this paper, we introduce a reduced order model-based reinforcement learning (MBRL) approach, utilizing the Iterative Linear Quadratic Regulator (ILQR) algorithm for the optimal control of nonlinear partial differential equations (PDEs).…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
Sequential quadratic programming (SQP) is widely used in solving nonlinear optimization problem, with advantages of warm-starting solutions, as well as finding high-accurate solution and converging quadratically using second-order…