Introduction to Convex Optimization

10-425 + 10-625, Fall 2023
School of Computer Science
Carnegie Mellon University


Important Notes

This schedule is tentative and subject to change. Please check back often.

Tentative Schedule

Date Lecture Readings Announcements

Theory I: Fundamentals

Mon, 28-Aug Lecture 1 : Overview of optimization
[Notes]

Wed, 30-Aug Lecture 2 : Overview of optimization / Convex Sets
[Notes]
  • Convex sets. Boyd & Vandenberghe (2004). Convex Optimization, Chapter 2.

Fri, 1-Sep

Mon, 4-Sep Labor Day

Wed, 6-Sep Lecture 3 : Convex sets
[Notes]
  • Convex sets. Boyd & Vandenberghe (2004). Convex Optimization, Chapter 2.

HW1 out (L1-L4)

Fri, 8-Sep Lecture 4 : Convex functions
[Notes]

Mon, 11-Sep Recitation: HW1

Wed, 13-Sep Lecture 5 : Convex functions / Smoothness
[Notes]

Algorithms I: First-order methods

Fri, 15-Sep Lecture 6 : Strong convexity / Optimality conditions
[Notes]

Sun, 17-Sep

HW1 due

Mon, 18-Sep Lecture 7 : Gradient descent
[Notes]

Wed, 20-Sep Lecture 8 : Convergence of gradient descent
[Notes]

Quiz 1 (in-class)

HW2 out (L5-L8)

Fri, 22-Sep Recitation: HW2

Mon, 25-Sep Lecture 9 : Convergence of GD / Subgradients
[Notes]
  • Subgradients. Boyd et al. (2022). Stanford EE364b lecture notes..

Wed, 27-Sep Lecture 10 : The subgradient method
[Notes]

Fri, 29-Sep (No Recitation)

Sun, 1-Oct

HW2 due

Mon, 2-Oct Lecture 11 : Projected gradient descent
[Notes]

HW3 out (L9-L12)

Wed, 4-Oct Lecture 12 : Stochastic gradient descent
[Notes]

(Quiz 2 in-class)

Fri, 6-Oct Recitation: HW3

Mon, 9-Oct Lecture 13 : Convergence of SGD
[Notes]

Theory II: Duality

Wed, 11-Oct Lecture 14 : Duality in linear programs
[Notes]

(Quiz 3 in-class)

Thu, 12-Oct

HW3 due

Fri, 13-Oct (No Recitation)

Mon, 16-Oct Fall break

Tue, 17-Oct

Wed, 18-Oct Fall break

Thu, 19-Oct

Fri, 20-Oct Fall break

Mon, 23-Oct Lecture 15 : Lagrangian duality
[Notes]

HW4 out (L13-L16)

Algorithms II: Second-order methods

Wed, 25-Oct Lecture 16 : Newton's method / Log-barrier method
[Notes]

Fri, 27-Oct Recitation: HW4

Mon, 30-Oct Lecture 17 : Newton's method analysis
[Notes]

Wed, 1-Nov Lecture 18 : Quasi-Newton methods / KKT conditions
[Notes]

(Quiz 4 in-class)

Thu, 2-Nov

Fri, 3-Nov (No Recitation)

HW4 due

Mon, 6-Nov (Lecture cancelled)

Wed, 8-Nov In-class Exam

Project description out

Fri, 10-Nov (Discussions with instructor about project ideas)

Algorithms III: Advanced methods

Mon, 13-Nov Lecture 19 : Proximal gradient descent
[Notes]

Project team formation due by 2pm

Wed, 15-Nov Lecture 20 : Momentum / Nesterov Acceleration
[Notes]

Thu, 16-Nov

Project proposal due

Fri, 17-Nov

Sat, 18-Nov

HW625 out

Mon, 20-Nov Lecture 21 : Adaptive gradient methods / Mirror Descent / AdaGrad
[Notes]

(Quiz 5 in-class)

Wed, 22-Nov Thanksgiving Holiday- No class

Thu, 23-Nov Thanksgiving Holiday- No class

Fri, 24-Nov Thanksgiving Holiday- No class

Mon, 27-Nov Lecture 22 : Adaptive gradient methods / RMSProp / Adam / Regret minimization
[Notes]

Wed, 29-Nov (Lecture rescheduled to Friday)

Thu, 30-Nov

Project checkpoint due

Fri, 1-Dec Lecture 23 : Online gradient descent / Parallel and distributed SGD
[Notes]

Nonconvex optimization

Mon, 4-Dec Lecture 24 : Parallel and distributed SGD / (Nearly)-convex optimization
[Notes]

HW625 due

Wed, 6-Dec Lecture 25 : Theories of non-convex optimization / Special topics: Optimization and ML
[Notes]

Fri, 8-Dec

Sun, 10-Dec

Project poster due

Tue, 12-Dec Project Final Presentations (details will be announced on Piazza)

Wed, 13-Dec

Project final report due