Gateaux derivative

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Related lectures (31)

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Optimal Control Theory: Basics

Covers the fundamentals of optimal control theory, focusing on defining OCPs, existence of solutions, performance criteria, physical constraints, and the principle of optimality.

Directional Derivatives: Definition and Applications

Explains the concept of directional derivatives and their applications in differentiating functions.

Descent methods and line search: First Wolfe condition

Introduces the First Wolfe condition to ensure a proportional decrease in the objective function relative to the step length.

Gradient: Scalar Field

Explores gradient in scalar fields, directional derivatives, and level sets.

Tangent Planes and Derivatives

Explores directional derivatives, tangent planes, and normal vectors in surfaces.

Surjectivity of Derivative Application

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Exact Fields, Direct Methods, Sobolev Spaces

Covers Hilbert's theorem, direct methods, and Sobolev spaces, including classical and modern methods.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Advanced Analysis II: Hessians and Directional Derivatives

Explores Hessians, directional derivatives, and function continuity in advanced analysis.

Objective function, Differentiability, the first order

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.