Lecture

Convexity and Optimization

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the concepts of convexity and optimization, focusing on the second derivative and its relation to the convexity of a function. The instructor explains how to determine convex and concave intervals by analyzing the sign of the second derivative. The lecture also delves into the application of these principles in finding maximum and minimum points of a function on a compact interval, using an algorithm to identify critical points. Examples are provided to illustrate the practical application of these mathematical concepts.

Official source

Ontological neighbourhood

Mathematics

Analysis: Calculus

Related concepts (32)

Display device

A display device is an output device for presentation of information in visual or tactile form (the latter used for example in tactile electronic displays for blind people). When the input information that is supplied has an electrical signal the display is called an electronic display. Common applications for electronic visual displays are television sets or computer monitors. Electronic visual display These are the technologies used to create the various displays in use today.

Plasma display

A plasma display panel (PDP) is a type of flat panel display that uses small cells containing plasma; ionized gas that responds to electric fields. Plasma televisions were the first large (over 32 inches diagonal) flat panel displays to be released to the public. Until about 2007, plasma displays were commonly used in large televisions. By 2013, they had lost nearly all market share due to competition from low-cost LCDs and more expensive but high-contrast OLED flat-panel displays.

Flexible display

A flexible display or rollable display is an electronic visual display which is flexible in nature, as opposed to the traditional flat screen displays used in most electronic devices. In recent years there has been a growing interest from numerous consumer electronics manufacturers to apply this display technology in e-readers, mobile phones and other consumer electronics. Such screens can be rolled up like a scroll without the image or text being distorted.

Flat-panel display

A flat-panel display (FPD) is an electronic display used to display visual content such as text or images. It is present in consumer, medical, transportation, and industrial equipment. Flat-panel displays are thin, lightweight, provide better linearity and are capable of higher resolution than typical consumer-grade TVs from earlier eras. They are usually less than thick. While the highest resolution for consumer-grade CRT televisions was 1080i, many flat-panel displays in the 2020s are capable of 1080p and 4K resolution.

3D display

A 3D display is a display device capable of conveying depth to the viewer. Many 3D displays are stereoscopic displays, which produce a basic 3D effect by means of stereopsis, but can cause eye strain and visual fatigue. Newer 3D displays such as holographic and light field displays produce a more realistic 3D effect by combining stereopsis and accurate focal length for the displayed content. Newer 3D displays in this manner cause less visual fatigue than classical stereoscopic displays.

Related lectures (64)

Derivability and Continuity

Explores derivability and continuity of functions, showcasing examples of functions with differentiability properties.

Elementary Functions and Derivatives

Covers elementary functions, derivatives, limits, continuity, and differentiability.

Limit Superior and Inferior: Convergence and Boundedness

Explains the concept of limit superior and limit inferior for bounded sequences.

Sequences: Limits and Convergence

Explores upper and lower limits of sequences and their convergence.

Tangent to Graph of a Function