Mathematical optimization | Multiple-criteria decision analysis
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective optimization has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives. Minimizing cost while maximizing comfort while buying a car, and maximizing performance whilst minimizing fuel consumption and emission of pollutants of a vehicle are examples of multi-objective optimization problems involving two and three objectives, respectively. In practical problems, there can be more than three objectives. For a nontrivial multi-objective optimization problem, no single solution exists that simultaneously optimizes each objective. In that case, the objective functions are said to be conflicting. A solution is called nondominated, Pareto optimal, Pareto efficient or noninferior, if none of the objective functions can be improved in value without degrading some of the other objective values. Without additional subjective preference information, there may exist a (possibly infinite) number of Pareto optimal solutions, all of which are considered equally good. Researchers study multi-objective optimization problems from different viewpoints and, thus, there exist different solution philosophies and goals when setting and solving them. The goal may be to find a representative set of Pareto optimal solutions, and/or quantify the trade-offs in satisfying the different objectives, and/or finding a single solution that satisfies the subjective preferences of a human decision maker (DM). Bicriteria optimization denotes the special case in which there are two objective functions. (Wikipedia).
Intro Into Multi Objective Optimization
Multi-objective optimization (also known as multi-objective programming, vector optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective func
From playlist Software Development
13_2 Optimization with Constraints
Here we use optimization with constraints put on a function whose minima or maxima we are seeking. This has practical value as can be seen by the examples used.
From playlist Advanced Calculus / Multivariable Calculus
13_1 An Introduction to Optimization in Multivariable Functions
Optimization in multivariable functions: the calculation of critical points and identifying them as local or global extrema (minima or maxima).
From playlist Advanced Calculus / Multivariable Calculus
Continuous multi-fidelity optimization
This video is #8 in the Adaptive Experimentation series presented at the 18th IEEE Conference on eScience in Salt Lake City, UT (October 10-14, 2022). In this video, Sterling Baird @sterling-baird presents on continuous multifidelity optimization. Continuous multi-fidelity optimization is
From playlist Optimization tutorial
This video is #7 in the Adaptive Experimentation series presented at the 18th IEEE Conference on eScience in Salt Lake City, UT (October 10-14, 2022). In this video, Sterling Baird @sterling-baird presents on multiobjective optimization where a pareto front of non-dominated solutions can
From playlist Optimization tutorial
11_2_1 The Geomtery of a Multivariable Function
Understanding the real-life 3D meaning of a multivariable function.
From playlist Advanced Calculus / Multivariable Calculus
Solving an equation with variables on both side and one solution
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist Solve Multi-Step Equations......Help!
Solving a multi-step equation by multiplying by the denominator
👉 Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
11_3_1 The Gradient of a Multivariable Function
Using the partial derivatives of a multivariable function to construct its gradient vector.
From playlist Advanced Calculus / Multivariable Calculus
Stanford CS330: Deep Multi-task and Meta Learning | 2020 | Lecture 2 - Multi-Task Learning
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/3vM17K0 This lecture covers: Multi-Task Learning -Problem Statement -Models, objectives, optimization -Challenges -Case study of real-world multi learning Transfer
From playlist Stanford CS330: Deep Multi-task and Meta Learning | Autumn 2020
If You Give a Mouse (two) Loss Functions : Multi Objective Optimization
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From playlist Explainers
Discrete multi-fidelity optimization
This video is #9 in the Adaptive Experimentation series presented at the 18th IEEE Conference on eScience in Salt Lake City, UT (October 10-14, 2022). In this video, Sterling Baird @sterling-baird presents on discrete multi-fidelity optimization. In discrete multi-fidelity optimization, t
From playlist Optimization tutorial
Lecture 7 | Convex Optimization I
Professor Stephen Boyd, of the Stanford University Electrical Engineering department, expands upon his previous lectures on convex optimization problems for the course, Convex Optimization I (EE 364A). Convex Optimization I concentrates on recognizing and solving convex optimization pro
From playlist Lecture Collection | Convex Optimization
The Optimality of the Interleaving Distance on Multidimensional... Modules - Michael Lesnick
Michael Lesnick Stanford University; Member, School of Mathematics, IAS March 6, 2013 Persistent homology is a central object of study in applied topology. It offers a flexible framework for defining invariants, called barcodes, of point cloud data and of real valued functions. Many of the
From playlist Mathematics
Fixing GAN optimization through competitive gradient descent - Anima Anandkumar
Workshop on Theory of Deep Learning: Where next? Topic: Fixing GAN optimization through competitive gradient descent Speaker: Anima Anandkumar Affiliation: Caltech Date: October 15, 2019 For more video please visit http://video.ias.edu
From playlist Workshop on Theory of Deep Learning: Where next?
11_3_6 Continuity and Differentiablility
Prerequisites for continuity. What criteria need to be fulfilled to call a multivariable function continuous.
From playlist Advanced Calculus / Multivariable Calculus
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 41-VMLS multi objective LS
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares