# Semidefinite Relaxation-Based Optimization of Multiple-Input Wireless Power Transfer Systems

## TL;DR

This paper introduces a semidefinite relaxation-based convex optimization method for multi-transmitter wireless power transfer systems, ensuring physical realizability and global optimality, which improves upon traditional nonconvex approaches.

## Contribution

The paper presents a novel convex optimization framework using tight semidefinite relaxation for designing physically realizable multi-transmitter WPT systems, guaranteeing global optimality.

## Key findings

- The method reliably finds the true global optimum.
- Numerical results validate the effectiveness and practicality of the approach.
- The approach outperforms traditional methods like genetic algorithms.

## Abstract

An optimization procedure for multi-transmitter (MISO) wireless power transfer (WPT) systems based on tight semidefinite relaxation (SDR) is presented. This method ensures physical realizability of MISO WPT systems designed via convex optimization -- a robust, semi-analytical and intuitive route to optimizing such systems. To that end, the nonconvex constraints requiring that power is fed into rather than drawn from the system via all transmitter ports are incorporated in a convex semidefinite relaxation, which is efficiently and reliably solvable by dedicated algorithms. A test of the solution then confirms that this modified problem is equivalent (tight relaxation) to the original (nonconvex) one and that the true global optimum has been found. This is a clear advantage over global optimization methods (e.g. genetic algorithms), where convergence to the true global optimum cannot be ensured or tested. Discussions of numerical results yielded by both the closed-form expressions and the refined technique illustrate the importance and practicability of the new method. It, is shown that this technique offers a rigorous optimization framework for a broad range of current and emerging WPT applications.