# A Sequential Quadratic Programming Method for Constrained Multi-objective Optimization Problems

## TL;DR

This paper introduces a globally convergent sequential quadratic programming method tailored for constrained multi-objective optimization, effectively handling inequality constraints and ensuring convergence to critical points.

## Contribution

It develops a novel SQP algorithm that guarantees feasibility and convergence for multi-objective problems with inequality constraints, using a non-differentiable penalty function.

## Key findings

- Method converges to critical points under mild assumptions
- Compared favorably with existing methods on test problems
- Ensures feasible descent directions at each iteration

## Abstract

In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear approximation of all objective functions as well as constraint functions. The sub-problem at every iteration of the sequence has feasible solution. A non-differentiable penalty function is used to deal with constraint violations. A descent sequence is generated which converges to a critical point under the Mangasarian-Fromovitz constraint qualification along with some other mild assumptions. The method is compared with a selection of existing methods on a suitable set of test problems.