arXiv subjects

Luoyi Tao

Publications and source records attributed to Luoyi Tao.

3 recordsLinked to original sources

arXiv2026

Distributed Computing for Huge-Scale Aggregative Convex Programming

Concerning huge-scale aggregative convex programming of a linear objective subject to the affine constraints of equality and inequality and the quadratic constraints of inequality, convex and aggregatively computable, an algorithm is developed for its distributed computing. The consensus with single common variable is used to partition the constraints into multi-consensus blocks, and the subblocks of each consensus block are employed to partition the primal variables into multiple sets of disjoint subvectors. The global consensus constraints of equality and the original constraints are converted into the extended constraints of equality via slack variables to help initialize the algorithm. The augmented Lagrangian, the proximal point method with double proximal terms or single, the block-coordinate Gauss-Seidel method, and ADMM are used to update the primal and slack variable sequences; descent models with built-in bounds are used to update the dual, motivated by the mathematical structures of the first-order characteristics of the update rules for the primal and slack. The feasibility conditions for the algorithm to produce optimal solutions are described and their realizations through initial and parameter values are outlined. Under the feasibility conditions supposed, convergence of the algorithm to optimal solutions is argued and the rate of convergence, $O(1/k^{1/2})$ is estimated roughly. Issues requiring further explorations are listed.

math.OC↗

arXiv2025

Distributed Computing for Huge-Scale Linear Programming

This study develops an algorithm for distributed computing of linear programming problems of huge-scales. Global consensus with single common variable, multiblocks, and augmented Lagrangian are adopted. The consensus is used to partition the constraints of equality and inequality into multi-consensus blocks, and the subblocks of each consensus block are employed to partition the primal variables into $M$ sets of disjoint subvectors. The global consensus constraints of equality and other constraints are replaced equivalently by the extended constraints of equality involving slack variables, since the slack variables help the feasibility and initialization of the algorithm. The block-coordinate Gauss-Seidel method, the proximal point method, and ADMM are used to update the primal variables, descent models used to update the dual. Convergence of the algorithm to optimal solutions is argued and the rate of convergence, $O(1/k^{1/2})$ is estimated, under feasibility of the algorithm and boundedness of the dual sequences supposed. Analysis is presented on how to ensure the feasibility and boundedness through initial and control parameter values and a dual descent model with built-in bound for the original constraints of inequality. Further exploration of dual descent models with built-in bound is needed.

math.OC↗

arXiv2020

Homogeneous shear turbulence as a second-order cone program

To help resolve issues of non-realizability and restriction to homogeneity faced by analytical theories of turbulence, we explore three-dimensional homogeneous shear turbulence of incompressible Newtonian fluids via optimal control and convex optimization. The framework is composed of multi-point spatial correlations of velocity and pressure fluctuations up to the degenerate fourth order, their evolution equations and constraints. The integral of trace of the second order correlations is argued as the objective functional to be maximized. The sources of the constraints are discussed like the Cauchy-Schwarz inequality and the non-negativity of variance of products (NNVP). Two models are defined: the second-order model uses the contracted and degenerate third order correlations as control variables; the third-order model takes the degenerate fourth order correlations as control variables. Both are second-order cone programs. Computation of large-scale and huge-scale and link to big data are noted. The exponential growth rates of the asymptotic states are bounded from above by zero. The steady state of the second-order model is solved. Three finite macro length scales are predicted beyond which the two-point correlations are negligible. The predicted values of the anisotropy tensor are consistent with experimental data qualitatively (concerning the relative numerical order of the diagonal components), albeit with large quantitative differences attributed to the non-enforceability of NNVP within the model. Compared with DNS data, the predicted second order correlation functions contain flawed features of local minima too large in magnitude or present spuriously. The third-order model is expected to improve predictions, owing to its ability to include constraints from NNVP and its formulation in an enlarged control variable space. It is yet open how to solve this huge-scale problem.

physics.flu-dyn↗