• Description: Process Optimisation
• Lecturer: M. Kvasnica
• Language: English

Topics

• Gradient-Free Unconstrained Optimization Methods
  • Quiz and repetition (29 min)
  • Random search: The Luus-Jaakola method (21 min)
  • Random search: Simulated annealing (18 min)
  • The extremum seeking method (29 min)
  • The Nelder-Mead method (39 min)
• Equality-Constrained Optimization
  • The elimination method - general idea (13 min)
  • Elimination of linear equations (27 min)
  • Linear independence (8 min)
  • Elimination of nonlinear equations (5 min)
  • Example: Optimal network flow (12 min)
  • The Lagrange method (24 min)
  • Lagrange method applied to equality-constrained quadratic programs (15 min)
  • Lagrange method applied to equality-constrained quadratic programs (ctd.) (5 min)
  • Necessary condition of linear independence (6 min)
  • Economic interpretation of Lagrange multipliers (11 min)
  • Economic interpretation of Lagrange multipliers (ctd.) (13 min)
• Equality-constrained quadratic programming
  • Lagrange method (10 min)
  • Feasible start Newton method (24 min)
  • Feasible start Newton method (ctd.) (4 min)
  • Infeasible start Newton method (8 min)
• Inequality-constrained optimization
  • Typical examples (8 min)
  • Active and non-active constraints (9 min)
  • The Karush-Kuhn-Tucker optimality conditions (ctd.) (8 min)
  • Degeneracy and complexity of optimization problems (23 min)
  • Inequality-constrained quadratic programming - active set method (14 min)
  • Inequality-constrained quadratic programming - active set method (ctd.) (33 min)
  • Active set method: example (9 min)
  • Quadprog (4 min)
• Linear programming
  • Problem formulation and typical examples (21 min)
  • Problem formulation and typical examples (ctd.) (4 min)
  • Graphical intepretation and complexity of LPs (6 min)
  • The simplex method (37 min)
  • The simplex method - graphical interpretation and summary (4 min)
  • Linprog (4 min)
  • Surprises of the simplex method - impact of heuristics (11 min)
  • Surprises of the simplex method - multiple optima (14 min)
  • Surprises of the simplex method - unboundedness (14 min)
  • Surprises of the simplex method - infeasibility (10 min)
• Quadratic programming
  • Problem formulation (11 min)
  • Unconstrained quadratic programming (5 min)
  • Equality-constrained quadratic programming (7 min)
  • Inequality-constrained quadratic programming - the KKT method (13 min)
• Applications: constrained fitting
  • Introduction (15 min)
  • Applications: sparse fitting (19 min)
  • Applications: separation and classification (8 min)
  • Linear separation (25 min)
  • Robust separation (13 min)
  • Approximate separation (6 min)
  • Approximate separation (ctd.) (7 min)
  • Support vector machines (18 min)
• Nonlinear optimization
  • Introduction (8 min)
  • Sequential quadratic programming (19 min)
• Integer optimization
  • Introduction (9 min)
  • Binary optimization problems (14 min)
  • Classification of integer problems (6 min)
  • Applications: knapsack problem, resources allocation (24 min)
  • Applications: traveling salesman problem (8 min)
  • Applications: warehouse location problem (19 min)
  • Applications: logic constraints (19 min)
  • Applications: logic constraints (ctd.) (43 min)
  • Applications: mixed constraints (35 min)
  • Applications: cardinality minimization (13 min)
  • Algorithms for integer optimization: extensive enumeration (12 min)

Lectures

• Lecture 2: 07.10.2014, duration: 97 min
  • Quiz and repetition (29 min)
  • Random search: The Luus-Jaakola method (21 min)
  • Random search: Simulated annealing (18 min)
  • The extremum seeking method (29 min)
• Lecture 3: 14.10.2014, duration: 92 min
  • The Nelder-Mead method (39 min)
  • The elimination method - general idea (13 min)
  • Elimination of linear equations (27 min)
  • Linear independence (8 min)
  • Elimination of nonlinear equations (5 min)
• Lecture 4: 21.10.2014, duration: 73 min
  • Example: Optimal network flow (12 min)
  • The Lagrange method (24 min)
  • Lagrange method applied to equality-constrained quadratic programs (15 min)
  • Lagrange method applied to equality-constrained quadratic programs (ctd.) (5 min)
  • Necessary condition of linear independence (6 min)
  • Economic interpretation of Lagrange multipliers (11 min)
• Lecture 5: 28.10.2014, duration: 76 min
  • Economic interpretation of Lagrange multipliers (ctd.) (13 min)
  • Lagrange method (10 min)
  • Feasible start Newton method (24 min)
  • Feasible start Newton method (ctd.) (4 min)
  • Infeasible start Newton method (8 min)
  • Typical examples (8 min)
  • Active and non-active constraints (9 min)
• Lecture 6: 04.11.2014, duration: 107 min
  • The Karush-Kuhn-Tucker optimality conditions (ctd.) (8 min)
  • Degeneracy and complexity of optimization problems (23 min)
  • Problem formulation and typical examples (21 min)
  • Problem formulation and typical examples (ctd.) (4 min)
  • Graphical intepretation and complexity of LPs (6 min)
  • The simplex method (37 min)
  • The simplex method - graphical interpretation and summary (4 min)
  • Linprog (4 min)
• Lecture 7: 11.11.2014, duration: 85 min
  • Surprises of the simplex method - impact of heuristics (11 min)
  • Surprises of the simplex method - multiple optima (14 min)
  • Surprises of the simplex method - unboundedness (14 min)
  • Surprises of the simplex method - infeasibility (10 min)
  • Problem formulation (11 min)
  • Unconstrained quadratic programming (5 min)
  • Equality-constrained quadratic programming (7 min)
  • Inequality-constrained quadratic programming - the KKT method (13 min)
• Lecture 8: 18.11.2014, duration: 94 min
  • Inequality-constrained quadratic programming - active set method (14 min)
  • Inequality-constrained quadratic programming - active set method (ctd.) (33 min)
  • Active set method: example (9 min)
  • Quadprog (4 min)
  • Introduction (15 min)
  • Applications: sparse fitting (19 min)
• Lecture 9: 25.11.2014, duration: 104 min
  • Applications: separation and classification (8 min)
  • Linear separation (25 min)
  • Robust separation (13 min)
  • Approximate separation (6 min)
  • Approximate separation (ctd.) (7 min)
  • Support vector machines (18 min)
  • Introduction (8 min)
  • Sequential quadratic programming (19 min)
• Lecture 10: 02.12.2014, duration: 99 min
  • Introduction (9 min)
  • Binary optimization problems (14 min)
  • Classification of integer problems (6 min)
  • Applications: knapsack problem, resources allocation (24 min)
  • Applications: traveling salesman problem (8 min)
  • Applications: warehouse location problem (19 min)
  • Applications: logic constraints (19 min)
• Lecture 11: 09.12.2014, duration: 103 min
  • Applications: logic constraints (ctd.) (43 min)
  • Applications: mixed constraints (35 min)
  • Applications: cardinality minimization (13 min)
  • Algorithms for integer optimization: extensive enumeration (12 min)