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. |
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2 |
Convex sets Convex sets and cones; some common and important examples; operations that preserve convexity. |
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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. |
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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. |
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9 |
Filter design and equalization FIR filters; general and symmetric lowpass filter design; Chebyshev equalization; magnitude design via spectral factorization. |
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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. |
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11 |
Convex-cardinality problems and examples; |
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12 |
Total variation reconstruction; iterated re-weighted |
( 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. |
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15 |
Numerical linear algebra background Basic linear algebra operations; factor-solve methods; sparse matrix methods. |
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16 |
Unconstrained minimization Gradient and steepest descent methods; Newton method; self-concordance complexity analysis. |
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17 |
Equality constrained minimization Elimination method; Newton method; infeasible Newton method. |
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18 |
Interior-point methods Barrier method; sequential unconstrained minimization; self-concordance complexity analysis. |
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19 |
Disciplined convex programming and CVX Convex optimization solvers; modeling systems; disciplined convex programming; CVX. |
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20 | Conclusions |