Gradients and optimization with constraints in economics and social sciences

Despite their widespread use in advanced analytical and numerical techniques, gradient field methods are often underrepresented in the foundational training of economists and social scientists. As machine learning and sophisticated analytical and numerical approaches gain traction, the importance of gradient methods in optimization processes becomes increasingly apparent. This oversight in academic and practical toolsets is suboptimal. This paper aims to address this gap by introducing gradient field methods both intuitively and rigorously, situating them within the context of problems commonly encountered by economists and social scientists, with a particular focus on equality constrained optimization.