Convex separable problems with linear and box constraints in signal processing and communications

Abstract

In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through an iterative procedure in a finite number of steps. Graphical interpretations are given casting valuable insights into the proposed algorithm and allowing to retain some of the intuition spelled out by the water-filling policy. It turns out that it is not only general enough to compute the solution to different instances of the problem at hand but also remarkably simple in the way it operates. We also show how some power allocation problems in signal processing and communications can be solved with the proposed algorithm.

submitted to IEEE Trans. Signal Process

References in corpus (4)

• A Tutorial on the Optimization of Amplify-and-Forward MIMO Relay Systems
• Power Allocation in Two-Hop Amplify-and-Forward MIMO Relay Systems with QoS requirements
• Duality and Optimization for Generalized Multi-hop MIMO Amplify-and-Forward Relay Networks with Linear Constraints
• Separable convex optimization problems with linear ascending constraints

Cited by in corpus (8)

• Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems
• New Viewpoint and Algorithms for Water-Filling Solutions in Wireless Communications
• A Survey of Algorithms for Separable Convex Optimization with Linear Ascending Constraints
• On a reduction for a class of resource allocation problems
• Weighted Sum-Throughput Maximization for MIMO Broadcast Channel: Energy Harvesting Under System Imperfection
• Distributed Resource Allocation Over Random Networks Based on Stochastic Approximation
• Distributed Subgradient-based Multi-agent Optimization with More General Step Sizes
• Separable Convex Optimization with Nested Lower and Upper Constraints