Mathematical Foundations of Robust and Distributionally Robust Optimization

Share this & earn $10
Centre de recherches mathématiques - CRM
Published at : 27 Oct 2021
172 views
2
0

(13 septembre 2021 / September 13, 2021) Seminar Applied Mathematics/Mathématiques appliquées https://dms.umontreal.ca/~mathapp/abs2122/DanielKuhn.html

Daniel Kuhn (EPFL, Suisse) https://people.epfl.ch/daniel.kuhn
Mathematical Foundations of Robust and Distributionally Robust Optimization

Abstract : Robust and distributionally robust optimization are modeling paradigms for decision-making under uncertainty where the uncertain parameters are only known to reside in an uncertainty set or are governed by any probability distribution from within an ambiguity set, respectively, and a decision is sought that minimizes a cost function under the most adverse outcome of the uncertainty. In this paper, we develop a rigorous and general theory of robust and distributionally robust nonlinear optimization using the language of convex analysis. Our framework is based on a generalized `primal-worst-equals-dual-best’ principle that establishes strong duality between a semi-infinite primal worst and a non-convex dual best formulation, both of which admit finite convex reformulations. This principle offers an alternative formulation for robust optimization problems that may be computationally advantageous, and it obviates the need to mobilize the machinery of abstract semi-infinite duality theory to prove strong duality in distributionally robust optimization. We illustrate the modeling power of our approach through convex reformulations for distributionally robust optimization problems whose ambiguity sets are defined through general optimal transport distances, which generalize earlier results for Wasserstein ambiguity sets.

mathCentre de recherches mathématiquesUniversité de Montréal

Eve - Give It To You (Official Music Video) ft. Sean Paul

Eve - Give It To You (Official Music Video) ft. Sean Paul

Videos for Toddlers with Blippi | Learn Colors and Numbers for Children

Videos for Toddlers with Blippi | Learn Colors and Numbers for Children

Your best option refeeld (1 hour version)

Your best option refeeld (1 hour version)

"YOU WON'T DO IT" Challenge for $1000 with the Norris Nuts

"YOU WON'T DO IT" Challenge for $1000 with the Norris Nuts

😭DUPING IS BACK IN PET SIMULATOR X?! *GAME BREAKING* (Roblox)

😭DUPING IS BACK IN PET SIMULATOR X?! *GAME BREAKING* (Roblox)

sawing a big oak log

sawing a big oak log

A Higher Place - Adam Levine

A Higher Place - Adam Levine

Learning How To Say No Is An Invaluable Skill - Jacob Morgan

Learning How To Say No Is An Invaluable Skill - Jacob Morgan

Kung Pow! Enter the Fist: It will be significant.

Kung Pow! Enter the Fist: It will be significant.

Best Gymnastics & Flexibility TikTok Videos January 2021 - Amazing Gymnastics Skills

Best Gymnastics & Flexibility TikTok Videos January 2021 - Amazing Gymnastics Skills

What is CONTROVERSY? What does CONTROVERSY mean? CONTROVERSY meaning, definition & explanation

What is CONTROVERSY? What does CONTROVERSY mean? CONTROVERSY meaning, definition & explanation

Kids Stretching And Flexibility - Pilates, Yoga and Balance

Kids Stretching And Flexibility - Pilates, Yoga and Balance

The History of the Greenback Party

The History of the Greenback Party

Learn how to sew a hole on your shirt in an amazing way / amazing repairs to clothes

Learn how to sew a hole on your shirt in an amazing way / amazing repairs to clothes

Expressions for talking about quantity | Learn English with Cambridge

Expressions for talking about quantity | Learn English with Cambridge

Ariana Grande, Doja Cat - motive (audio)

Ariana Grande, Doja Cat - motive (audio)

Sci-Fi Short Film “Populace" | DUST Exclusive

Sci-Fi Short Film “Populace" | DUST Exclusive

Alexander "Academics" Juneblad - Journal III (ang. Kilskrift)

Alexander "Academics" Juneblad - Journal III (ang. Kilskrift)

Close To Permit

Close To Permit

SNAP! - The Power (Official Video)

SNAP! - The Power (Official Video)

Ship Launch | 10 Awesome Waves, FAILS and CLOSE CALLS

Ship Launch | 10 Awesome Waves, FAILS and CLOSE CALLS

KAIRI USED LANCELOT AND DID AN UNLIMITED DASH

KAIRI USED LANCELOT AND DID AN UNLIMITED DASH

A Look Inside an Exquisite Countryside Estate | At Home with Katharine Pooley | Harper's BAZAAR

A Look Inside an Exquisite Countryside Estate | At Home with Katharine Pooley | Harper's BAZAAR

20 ways to beautify with a scarf + The best way to wear a scarf #Part2

20 ways to beautify with a scarf + The best way to wear a scarf #Part2

Very Same Power-Ricardo Sanchez

Very Same Power-Ricardo Sanchez

Feargal Sharkey - A Good Heart (Enhanced Audio Original Video Clip)

Feargal Sharkey - A Good Heart (Enhanced Audio Original Video Clip)

DeDe Negra - Think About You

DeDe Negra - Think About You

Reverse Engineering a UFO | National Geographic

Reverse Engineering a UFO | National Geographic

Great Idea - How to Make a Planter Pot From Cement And Fabric

Great Idea - How to Make a Planter Pot From Cement And Fabric

functioning from the wrong mind in Christ

functioning from the wrong mind in Christ

How Pro Bassists Learn Literally THOUSANDS Of Songs (It’s Simpler Than You Think)

How Pro Bassists Learn Literally THOUSANDS Of Songs (It’s Simpler Than You Think)

Roots Remain

Roots Remain

Tessa Violet - Crush (Official Music Video)

Tessa Violet - Crush (Official Music Video)

How to make diseases disappear | Rangan Chatterjee | TEDxLiverpool

How to make diseases disappear | Rangan Chatterjee | TEDxLiverpool

Blake Lively Funniest Moments

Blake Lively Funniest Moments

Tips for Starting a Healthy Lifestyle!

Tips for Starting a Healthy Lifestyle!

RICH VS POOR BABY - Swap the Child - Scary Teacher 3D | BuzzStar

RICH VS POOR BABY - Swap the Child - Scary Teacher 3D | BuzzStar

International Relations: An Introduction

International Relations: An Introduction

HOW I BEAT TENZ IN TWITCH RIVALS !?! ($12,000)

HOW I BEAT TENZ IN TWITCH RIVALS !?! ($12,000)

Melanie Martinez - The Principal (Lyrics)

Melanie Martinez - The Principal (Lyrics)

Brush Your Teeth | Kids Songs |  Super Simple Songs

Brush Your Teeth | Kids Songs | Super Simple Songs

Snoop Dogg, Ice Cube, Dr. Dre - Imagine ft. The Game, 2Pac

Snoop Dogg, Ice Cube, Dr. Dre - Imagine ft. The Game, 2Pac

#HopeShifah akabidekko Mercy Owe Dubai amazigga oluvanyuma lwokufelebwa Omwamiwe Jimmy #Surprise

#HopeShifah akabidekko Mercy Owe Dubai amazigga oluvanyuma lwokufelebwa Omwamiwe Jimmy #Surprise

How To Draw A Toilet

How To Draw A Toilet

Kid FAKES SICK for new Roblox Game. Big Surprise at the End.

Kid FAKES SICK for new Roblox Game. Big Surprise at the End.

Fifty Two Gaj Ka Daman । Pranjal Dahiya । Aman Jaji । Renuka Panwar । Hariyanavi Song । New Version

Fifty Two Gaj Ka Daman । Pranjal Dahiya । Aman Jaji । Renuka Panwar । Hariyanavi Song । New Version

B Young - Differences (Official Lyric Video)

B Young - Differences (Official Lyric Video)

There's an X for That | 2021 X Range | BMW USA

There's an X for That | 2021 X Range | BMW USA

A CASUAL DAY AT THE OFFICE | Christos lefas

A CASUAL DAY AT THE OFFICE | Christos lefas