Optimization aims to find the values of variables that maximize or minimize a given objective function, subject to certain constraints.

Linear programming problems involve linear objective functions and constraints, which can include linear equations, nonlinear equations, and inequalities.

The simplex method is an iterative algorithm used to find the optimal solution to a linear programming problem by moving from one vertex of the feasible region to another until the optimal solution is reached.

Gradient descent, conjugate gradient method, and Newton's method are all iterative methods commonly used for solving nonlinear programming problems.

The principle of optimality states that an optimal solution to a problem can be constructed from optimal solutions to its subproblems, which is a fundamental concept in dynamic programming.

Dijkstra's algorithm, Bellman-Ford algorithm, and Floyd-Warshall algorithm are all dynamic programming algorithms commonly used for solving shortest path problems.

The feasible region is the region in the decision space that satisfies all the constraints of an optimization problem.

The optimal solution is the point in the feasible region that optimizes the objective function, either maximizing or minimizing it.

The gradient is a vector that contains the partial derivatives of the objective function with respect to each decision variable, indicating the direction of the greatest rate of change.

Decomposition is the process of breaking a problem down into smaller, more manageable subproblems, which are then solved independently.

Approximation is the process of finding a solution that is close to the optimal solution, but not necessarily the exact optimal solution.

Slack variables are introduced to convert inequality constraints into equality constraints, which is necessary for the simplex method to be applied.

A stationary point is a point where the gradient of the objective function is zero, which indicates that the function is neither increasing nor decreasing at that point.

Memoization is the process of storing the solutions to subproblems so that they can be reused later, which can significantly improve the efficiency of the dynamic programming algorithm.

Global optimization is the process of finding the global minimum or maximum of a function over a given domain, which is typically more challenging than finding a local minimum or maximum.