Mathematical Foundations · Multivariable Calculus

Multivariable Calculus: Optimization in R^n

Public introduction · full guide in Eikos

Introduction

What this guide covers

A rigorous treatise on the theory of free and conditioned extremes: from topology and Karush-Kuhn-Tucker conditions to Lagrangian duality and second-order criteria.

Overview

Topics covered

  • Introduction
  • Mathematical Optimization in
  • Fundamentals of Topology and Differential Calculus
  • 1.1 Topological Structure and the Weierstrass Theorem
  • 1.2 Differentiability, Gradient Vector and Hessian Matrix
  • 1.3 Taylor formula in several variables

Related concepts

Main connections

  • Linear algebra & matrices
  • Calculus & differentiation
  • Time series & ARIMA
  • Supervised machine learning
  • Mathematical optimization & gradients
  • Conditional probability & independence

Compatible notation

Mathematical sample in LaTeX

The expression is rendered accessibly, with its LaTeX source preserved below.

f(x*)≤f(x)≤f(x*)∀x∈K
View LaTeX sourcef(x_{*}) \leq f(x) \leq f(x^{*}) \quad \forall x \in K