# A gradient descent akin method for constrained optimization: algorithms and applications

## TL;DR

This paper introduces GDAM, a new gradient descent-like method for constrained optimization, with proven convergence and demonstrated effectiveness in engineering applications like shape optimization and sensor network localization.

## Contribution

The paper develops a simplified, theoretically guaranteed gradient descent akin method (GDAM) for constrained optimization, expanding its applicability to large-scale engineering problems.

## Key findings

- GDAM is globally convergent under certain conditions.
- GDAM performs competitively on large, challenging engineering problems.
- The method is robust and adaptable to various constrained optimization scenarios.

## Abstract

We present a first-order method for solving constrained optimization problems. The method is derived from our previous work, a modified search direction method inspired by singular value decomposition. In this work, we simplify its computational framework to a ``gradient descent akin'' method (GDAM), i.e., the search direction is computed using a linear combination of the negative and normalized objective and constraint gradient. We give fundamental theoretical guarantees on the global convergence of the method. This work focuses on the algorithms and applications of GDAM. We present computational algorithms that adapt common strategies for the gradient descent method. We demonstrate the potential of the method using two engineering applications, shape optimization and sensor network localization. When practically implemented, GDAM is robust and very competitive in solving the considered large and challenging optimization problems.