MIT OpenCourseWare

Browse materialsMIT 6.079 · Fall 2009

Introduction to Convex Optimization

Subjects: Engineering · Mathematics

Art: Palmer, Edward, 1803-1872, Figures 113-123. Plate Electrical Machines, 1840 · Public domain

Instructors: Prof. Stephen Boyd, Prof. Pablo Parrilo
Term: Fall 2009
Level: Undergraduate
What's inside: 1 lecture note · 1 reading · 48 other files · 3 web pages
Materials open: MIT OCW

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About this course

Source: MIT OpenCourseWare 6.079 Introduction to Convex Optimization, Fall 2009, Prof. Stephen Boyd, Prof. Pablo Parrilo — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Convex Optimization · Convex Optimization Theory

How this course was organized

What's here, and what isn't

A lecture sequence of 20 items is confirmed. Assignment and exam materials exist too, but MIT's own order for them could not be verified, so they're shown as materials below rather than a sequence.

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MIT's page format for this item wasn't recognized clearly enough to place it safely. (6 items)
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Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

19 files

Assignments

18 files

Exams

11 files

MIT OpenCourseWare, Prof. Stephen Boyd, Prof. Pablo Parrilo, 6.079 Introduction to Convex Optimization, Fall 2009.

License: CC BY-NC-SA 4.0 · Edition: Fall 2009 · Open the original course on OCW ↗

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Introduction to Convex Optimization

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Assignments

Exams

Lecture 1: Introduction Mathematical optimization; least-squares and linear programming; convex optimization; course goals and topics; nonlinear optimization.

Lecture 2: Convex sets Convex sets and cones; some common and important examples; operations that preserve convexity.

Lecture 3: Convex functions Convex functions; common examples; operations that preserve convexity; quasiconvex and log-convex functions.

Lecture 4: Convex optimization problems Convex optimization problems; linear and quadratic programs; second-order cone and semidefinite programs; quasiconvex optimization problems; vector and multicriterion optimization.

Lecture 5: Duality Lagrange dual function and problem; examples and applications.

Lecture 6: Approximation and fitting Norm approximation; regularization; robust optimization.

Lecture 7: Statistical estimation Maximum likelihood and MAP estimation; detector design; experiment design.

Lecture 8: Geometric problems Projection; extremal volume ellipsoids; centering; classification; placement and location problems.

Lecture 9: Filter design and equalization FIR filters; general and symmetric lowpass filter design; Chebyshev equalization; magnitude design via spectral factorization.

Lecture 10: Miscellaneous applications Multi-period processor speed scheduling; minimum time optimal control; grasp force optimization; optimal broadcast transmitter power allocation; phased-array antenna beamforming; optimal receiver location.

Lecture 11: l ₁ methods for convex-cardinality problems Convex-cardinality problems and examples; l ₁ heuristic; interpretation as relaxation.

Lecture 12: l ₁ methods for convex-cardinality problems (cont.) Total variation reconstruction; iterated re-weighted l ₁; rank minimization and dual spectral norm heuristic.

Lecture 13: Stochastic programming Stochastic programming; “certainty equivalent” problem; violation/shortfall constraints and penalties; Monte Carlo sampling methods; validation.

Lecture 14: Chance constrained optimization Chance constraints and percentile optimization; chance constraints for log-concave distributions; convex approximation of chance constraints.

Lecture 15: Numerical linear algebra background Basic linear algebra operations; factor-solve methods; sparse matrix methods.

Lecture 16: Unconstrained minimization Gradient and steepest descent methods; Newton method; self-concordance complexity analysis.

Lecture 17: Equality constrained minimization Elimination method; Newton method; infeasible Newton method.

Lecture 18: Interior-point methods Barrier method; sequential unconstrained minimization; self-concordance complexity analysis.

Lecture 19: Disciplined convex programming and CVX Convex optimization solvers; modeling systems; disciplined convex programming; CVX.

Lecture 20: Conclusions