Related papers: Explicit continuation methods with L-BFGS updating…
The standard quadratic optimization problem (StQP) consists of minimizing a quadratic form over the standard simplex. Without convexity or concavity of the quadratic form, the StQP is NP-hard. This problem has many relevant real-life…
Large-scale unconstrained optimization is a fundamental and important class of, yet not well-solved problems in numerical optimization. The main challenge in designing an algorithm is to require a few storage locations or very inexpensive…
We present a modified limited memory BFGS (L-BFGS) method that converges globally and linearly for nonconvex objective functions. Its distinguishing feature is that it turns into L-BFGS if the iterates cluster at a point near which the…
Convex quadratic programming (QP) is an important class of optimization problem with wide applications in practice. The classic QP solvers are based on either simplex or barrier method, both of which suffer from the scalability issue…
In the calculation of Positron Emission Tomography (PET) image reconstruction, System Response Matrix (SRM) characterizes the numerical relationship between measurement space and image space. Due to a significant amount of calculation and…
Accurate prediction of rarefied gas flows is important for space vehicle design, particularly in rarefied regimes where the Navier-Stokes equations are no more valid. While the direct simulation Monte Carlo (DSMC) method acts as a numerical…
A novel approach to exploiting the log-convex structure present in many design problems is developed by modifying the classical Sequential Quadratic Programming (SQP) algorithm. The modified algorithm, Logspace Sequential Quadratic…
This paper presents a novel learning-based trajectory planning framework for quadrotors that combines model-based optimization techniques with deep learning. Specifically, we formulate the trajectory optimization problem as a quadratic…
Currently, the simplex method and the interior point method are indisputably the most popular algorithms for solving linear programs, LPs. Unlike general conic programs, LPs with a finite optimal value do not require strict feasibility in…
In this paper, we consider nonlinear optimization problems with a stochastic objective function and deterministic equality constraints. We propose an inexact two-stepsize stochastic sequential quadratic programming (SQP) algorithm and…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
Training recurrent neural networks is predominantly achieved via backpropagation through time (BPTT). However, this algorithm is not an optimal solution from both a biological and computational perspective. A more efficient and biologically…
We present a modified limited memory BFGS method with displacement aggregation (AggMBFGS) for solving nonconvex optimization problems. AggMBFGS refines curvature pair updates by removing linearly dependent variable variations, ensuring that…
To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…
Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By…
Update formulas for the Hessian approximations in quasi-Newton methods such as BFGS can be derived as analytical solutions to certain nearest-matrix problems. In this article, we propose a similar idea for deriving new limited memory…
We present a globally convergent SQP-type method with the least constraint violation for nonlinear semidefinite programming. The proposed algorithm employs a two-phase strategy coupled with a line search technique. In the first phase, a…
In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…
Large Language Models (LLMs) using Chain-of-Thought (CoT) prompting excel at complex reasoning but generate verbose thought processes with considerable redundancy, leading to increased inference costs and reduced efficiency. We introduce a…
Continual learning (CL) enables models to adapt to evolving data streams without catastrophic forgetting, a fundamental requirement for real-world AI systems. However, the current methods often depend on large replay buffers or heavily…