Abhinaash Tiwari
I am an undergraduate student in Computational Mathematics at Kathmandu University, with a primary academic interest in the mathematical analysis of constrained optimization problems. My work focuses on understanding optimization from a rigorous perspective, including feasibility geometry, non-convexity, optimality conditions, and the behavior of solutions under perturbations.
My current academic work involves the formal formulation and analysis of optimization problems arising in stochastic and numerical settings. In particular, I study how estimation error and structural constraints (such as sparsity and budget constraints) influence stability, sensitivity, and convergence properties of optimal solutions. While such problems often originate in applied contexts, my emphasis is on their theoretical structure rather than empirical performance.
This website serves as a collection of proof-oriented notes and short expository essays written in the style of lecture notes. The posts focus on foundational topics such as Lagrangian duality, Karush–Kuhn–Tucker conditions, penalty methods, and sensitivity analysis in optimization. Each post aims to present precise definitions, mathematical arguments, and, where appropriate, proofs or proof sketches.
These notes are part of my preparation for graduate study in mathematics, particularly in areas related to optimization theory, numerical analysis, and applied analysis. The intended audience is readers with a background in undergraduate real analysis and linear algebra.