Скачать с ютуб Deriving the KKT conditions for Inequality-Constrained Optimization | Introduction to Duality в хорошем качестве

Deriving the KKT conditions for Inequality-Constrained Optimization | Introduction to Duality

Equality-Constrained Optimization Problems can be solved by Lagrange Multipliers. How about Inequality-Constrained ones? Here are the notes: https://raw.githubusercontent.com/Cey... One could try to also just build the Lagrangian and then minimizing the (unconstrained) Lagrangian. However, this will result in finding an optimum that lies on the boundary of our feasible region. This will also signal that Inequality constraints are more difficult to handle than equality constraints. In this video we will derive the Karush-Kuhn-Tucker conditions that (together with regularity) are necessary in order to find an optimizer of the constrained problem. The path towards them will introduce the duality or the dual of the problem. Feel free to write a comment if something was unclear or if you have troubles understanding :) ------- 📝 : Check out the GitHub Repository of the channel, where I upload all the handwritten notes and source-code files (contributions are very welcome): https://github.com/Ceyron/machine-lea... 📢 : Follow me on LinkedIn or Twitter for updates on the channel and other cool Machine Learning & Simulation stuff:   / felix-koehler   and   / felix_m_koehler   💸 : If you want to support my work on the channel, you can become a Patreon here:   / mlsim   ------- Timestamps: 00:00 Introduction 00:33 Why not use the gradient of Lagrangian? 03:31 Recovering Target from Lagrangian 09:03 Transformation to unconstrained problem 10:30 Disclaimer: inf instead of min 11:20 Hint: We need the standard form 12:43 Min-Max Inequality 14:09 Duality 16:30 Primal and Dual 17:15 The Duality Gap 17:45 Regularity & Strong Duality 18:40 Assuming a regular problem 21:58 Deducing the KKT 23:10 KKT: Primal Feasibility 23:25 KKT: Stationarity 24:24 KKT: Dual Feasibility 24:49 KKT: Complimentary Slackness 25:16 Simplifying Complimentary Slackness 26:46 Summary KKT 27:03 Regularity & Constraint Qualification 28:58 Outro