Convex separable problems with linear and box constraints

TL;DR

This paper presents a method to solve a class of convex optimization problems with linear and box constraints in closed-form, facilitating efficient power allocation in signal processing and communications.

Contribution

It derives a closed-form solution for separable convex problems with linear and box constraints, enabling practical and efficient implementation.

Findings

Closed-form solutions for a broad class of convex problems.

Efficient computation of Lagrange multipliers in finite steps.

Application to power allocation in signal processing.

Abstract

In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of iterations. This allows us to bridge the gap between a wide family of power allocation problems of practical interest in signal processing and communications and their efficient implementation in practice.