An algorithm for optimization with disjoint linear constraints and its application for predicting rain

TL;DR

This paper introduces a specialized quadratic optimization algorithm tailored for problems with disjoint linear constraints, demonstrating its effectiveness in weather forecasting by reducing computational costs compared to traditional methods.

Contribution

The paper presents a novel algorithm that exploits problem structure for efficient quadratic optimization with disjoint constraints, applicable to high-dimensional weather prediction models.

Findings

Improves computational efficiency over general interior point methods.

Reduces computational burden in rain prediction models.

Effective for high-dimensional weather forecasting problems.

Abstract

A specialized algorithm for quadratic optimization (QO, or, formerly, QP) with disjoint linear constraints is presented. In the considered class of problems, a subset of variables are subject to linear equality constraints, while variables in a different subset are constrained to remain in a convex set. The proposed algorithm exploits the structure by combining steps in the nullspace of the equality constraint's matrix with projections onto the convex set. The algorithm is motivated by application in weather forecasting. Numerical results on a simple model designed for predicting rain show that the algorithm is an improvement on current practice and that it reduces the computational burden compared to a more general interior point QO method. In particular, if constraints are disjoint and the rank of the set of linear equality constraints is small, further reduction in computational costs can be achieved, making it possible to apply this algorithm in high dimensional weather forecasting problems.