- Joined
- 3/29/14
- Messages
- 6
- Points
- 13
If I had to pick one module out of these 4, which is most useful?
Designs and Analysis of Algorithms
(algorithm analysis i.e lower bound arguments, average case analysis, and the theory of NP-completeness, recurrences, basic algorithm paradigms (such as prune-and-search, dynamic programming, branch-and-bound, graph traversal, and randomised approaches), amortized analysis)
Nonlinear Programming
(Fundamentals, unconstrained optimization: one-dimensional search, Newton-Raphson method, gradient method, constrained optimization: Lagrangian multipliers method, Karush-Kuhn-Tucker optimality conditions, Lagrangian duality and saddle point optimality conditions, convex programming: Frank-Wolfe method.)
Linear and Network Optimisation
(Introduction to LP: solving 2-variable LP via graphical methods. Geometry of LP: polyhedron, extreme points, existence of optimal solution at extreme point. Development of simplex method: basic solution, reduced costs and optimality condition, iterative steps in a simplex method, 2-phase method and Big-M method. Duality: dual LP, duality theory, dual simplex method. Sensitivity Analysis. Network optimization problems: minimal spanning tree problems, shortest path problems, maximal flow problems, minimum cost flow problems, salesman problems and postman problems.)
Mathematical Modelling
(Introduction of modelling; dynamic (or ODE) models: population models, pendulum motion; electrical networks, chemical reaction, etc; optimization and discrete models: profit of company, annuity, etc; probability models: president election poll, random walk, etc; Model analysis: dimensional analysis, equilibrium and stability, bifurcation, etc; and some typical applications.)
Designs and Analysis of Algorithms
(algorithm analysis i.e lower bound arguments, average case analysis, and the theory of NP-completeness, recurrences, basic algorithm paradigms (such as prune-and-search, dynamic programming, branch-and-bound, graph traversal, and randomised approaches), amortized analysis)
Nonlinear Programming
(Fundamentals, unconstrained optimization: one-dimensional search, Newton-Raphson method, gradient method, constrained optimization: Lagrangian multipliers method, Karush-Kuhn-Tucker optimality conditions, Lagrangian duality and saddle point optimality conditions, convex programming: Frank-Wolfe method.)
Linear and Network Optimisation
(Introduction to LP: solving 2-variable LP via graphical methods. Geometry of LP: polyhedron, extreme points, existence of optimal solution at extreme point. Development of simplex method: basic solution, reduced costs and optimality condition, iterative steps in a simplex method, 2-phase method and Big-M method. Duality: dual LP, duality theory, dual simplex method. Sensitivity Analysis. Network optimization problems: minimal spanning tree problems, shortest path problems, maximal flow problems, minimum cost flow problems, salesman problems and postman problems.)
Mathematical Modelling
(Introduction of modelling; dynamic (or ODE) models: population models, pendulum motion; electrical networks, chemical reaction, etc; optimization and discrete models: profit of company, annuity, etc; probability models: president election poll, random walk, etc; Model analysis: dimensional analysis, equilibrium and stability, bifurcation, etc; and some typical applications.)
