Notes for Lecture 20 are not available on MIT OpenCourseWare.
| LEC # | TOPICS | LECTURE NOTES |
|---|---|---|
| 1 | Introduction Mathematical optimization; least-squares and linear programming; convex optimization; course goals and topics; nonlinear optimization. | (PDF) |
| 2 | Convex sets Convex sets and cones; some common and important examples; operations that preserve convexity. | (PDF) |
| 3 | Convex functions Convex functions; common examples; operations that preserve convexity; quasiconvex and log-convex functions. | (PDF) |
| 4 | Convex optimization problems Convex optimization problems; linear and quadratic programs; second-order cone and semidefinite programs; quasiconvex optimization problems; vector and multicriterion optimization. | (PDF) |
| 5 | Duality Lagrange dual function and problem; examples and applications. | (PDF) |
| 6 | Approximation and fitting Norm approximation; regularization; robust optimization. | (PDF) |
| 7 | Statistical estimation Maximum likelihood and MAP estimation; detector design; experiment design. | (PDF) |
| 8 | Geometric problems Projection; extremal volume ellipsoids; centering; classification; placement and location problems. | (PDF) |
| 9 | Filter design and equalization FIR filters; general and symmetric lowpass filter design; Chebyshev equalization; magnitude design via spectral factorization. | (PDF) |
| 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. | (PDF) |
| 11 | l1 methods for convex-cardinality problems Convex-cardinality problems and examples; l1 heuristic; interpretation as relaxation. | (PDF) |
| 12 | l1 methods for convex-cardinality problems (cont.) Total variation reconstruction; iterated re-weighted l1; rank minimization and dual spectral norm heuristic. | (PDF - 1.4MB) |
| 13 | Stochastic programming Stochastic programming; "certainty equivalent" problem; violation/shortfall constraints and penalties; Monte Carlo sampling methods; validation. | (PDF) |
| 14 | Chance constrained optimization Chance constraints and percentile optimization; chance constraints for log-concave distributions; convex approximation of chance constraints. | (PDF) |
| 15 | Numerical linear algebra background Basic linear algebra operations; factor-solve methods; sparse matrix methods. | (PDF) |
| 16 | Unconstrained minimization Gradient and steepest descent methods; Newton method; self-concordance complexity analysis. | (PDF) |
| 17 | Equality constrained minimization Elimination method; Newton method; infeasible Newton method. | (PDF) |
| 18 | Interior-point methods Barrier method; sequential unconstrained minimization; self-concordance complexity analysis. | (PDF) |
| 19 | Disciplined convex programming and CVX Convex optimization solvers; modeling systems; disciplined convex programming; CVX. | (PDF) |
| 20 | Conclusions |