Academic year 1997/98
Graphical presentation. Level curves. Partial derivatives. Quadratic forms. The chain rule. Implicit derivation. Homogeneous functions. Linear approximation.
Optimization and decision problems. Topological notions. Existence of optimum and Weierstrass' theorem. Local optima and first and second order conditions.
Convex sets. Convex and concave functions. Conditions for concavity and convexity.
Lagrange method. Global optimum: Application of Weierstrass' theorem and convexity criteria. Regular points. Generalized Lagrangian.
The Kuhn-Tucker conditions. Binding constraints in a point. Regular points. Interior and corner critical points.
State and control variables. Problems with discrete time. Euler's equation. Dynamic programming. Problems with continuous time. Theory of optimal control.