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Mathematical Optimization for Business
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Other Subject Area: Business
Instruction in: English
Course Code: 17674
Transcript Source: Partner Institution
Course Details: Level 300, 400
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Students are expected to have completed courses with contents in linear algebra, multivariable differential calculus, statistics, business administration and computer programming.
DESCRIPTION
Topic 1.1. Linear optimization (LO). Operations research; LO models; formulations and applications; computer-based solution.
Topic 1.2. Graphical solution; sensitivity analysis.
Topic 1.3. The fundamental theorem of LO; basic feasible solutions and vertices; the simplex method.
Topic 1.4. The two-phase simplex method; interior point methods.
Topic 1.5. Optimal network flow models.
Topic 1.6. More applications and examples.
Topic 2.1. Integer optimization models; linear relaxations; optimality gap; graphical and computer solution.
Topic 2.2. The Branch and Bound method.
Topic 2.3. Combinatorial optimization models; strengthening formulations; valid inequalities.
Topic 2.4. More applications and examples.
Topic 3.1: Unconstrained non-linear optimization (NLO). Motivation and examples; local and global optima; convexity; optimality conditions; numerical solution.
Topic 3.2. Equality-constrained NLO. Motivation and examples; Lagrange multipliers; optimality conditions; numerical solution.
Topic 3.3. Inequality-constrained NLO. Motivation and examples; Karush-Kuhn-Tucker multipliers; optimality conditions; numerical solution.
Topic 3.4. More applications and examples.
Topic 1.2. Graphical solution; sensitivity analysis.
Topic 1.3. The fundamental theorem of LO; basic feasible solutions and vertices; the simplex method.
Topic 1.4. The two-phase simplex method; interior point methods.
Topic 1.5. Optimal network flow models.
Topic 1.6. More applications and examples.
Topic 2.1. Integer optimization models; linear relaxations; optimality gap; graphical and computer solution.
Topic 2.2. The Branch and Bound method.
Topic 2.3. Combinatorial optimization models; strengthening formulations; valid inequalities.
Topic 2.4. More applications and examples.
Topic 3.1: Unconstrained non-linear optimization (NLO). Motivation and examples; local and global optima; convexity; optimality conditions; numerical solution.
Topic 3.2. Equality-constrained NLO. Motivation and examples; Lagrange multipliers; optimality conditions; numerical solution.
Topic 3.3. Inequality-constrained NLO. Motivation and examples; Karush-Kuhn-Tucker multipliers; optimality conditions; numerical solution.
Topic 3.4. More applications and examples.
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