In the ever-evolving landscape of finance, the quest for optimal portfolio management has been a continuous pursuit. The process of selecting the right mix of assets to maximize returns while minimizing risk has long been at the core of investment strategy. With the advent of computational tools and the availability of financial data, this endeavor has witnessed a paradigm shift. Today, investors and financial analysts have at their disposal a plethora of quantitative techniques and software applications for portfolio optimization, each with its own strengths and limitations. This thesis delves into the realm of portfolio optimization by exploring and comparing the efficacy of two distinct methodologies—Monte Carlo simulation and Sequential Least Squares Quadratic Programming (SLSQP)—in the context of stock portfolio management.