Nonlinear programming and statistical estimation — Advanced reference · Introduction

Introduction

What this guide covers

Introduction Introduction # OPERATIONS RESEARCH & MATHEMATICAL STATISTICS

Overview

Topics covered

Introduction
Nonlinear Programming and Statistical Estimation
Introduction: The Historical and Conceptual Intersection
Nonlinear Programming (NLP) Fundamentals
Convexity and the Curvature Tensor (Hessian)
Karush-Kuhn-Tucker (KKT) Optimality Conditions

Related concepts

Main connections

Compatible notation

Mathematical sample in LaTeX

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

\begin{aligned} \min_{\mathbf{x} \in \mathbb{R}^d} \quad & f(\mathbf{x}) \\ \text{subject to} \quad & g_i(\mathbf{x}) \le 0, \quad i = 1, \dots, m \\ & h_j(\mathbf{x}) = 0, \quad j = 1, \dots, p \end{aligned}

View LaTeX source

\begin{aligned}
    \min_{\mathbf{x} \in \mathbb{R}^d} \quad & f(\mathbf{x}) \\
    \text{subject to} \quad & g_i(\mathbf{x}) \le 0, \quad i = 1, \dots, m \\
    & h_j(\mathbf{x}) = 0, \quad j = 1, \dots, p
    \end{aligned}