Economics Notes
Optimization Filomena Garcia Optimization
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
Mathematical Economics - Part I Optimization
Filomena Garcia
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Fall 2009
Filomena Garcia
Optimization
Optimization Filomena Garcia Optimization
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
1 Optimization in Rn
Optimization Problems in Rn Optimization Problems in Parametric Form Optimization Problems: Some Examples The objectives of Optimization Theory
2 Existence of Solutions 3 Unconstrained Optima 4 Equality Constraints 5 Inequality Constraints 6 Convex Structures in Optimization Theory 7 Quasiconvexity in Optimization 8 Parametric Continuity: The Maximum Theorem 9 Supermodularity and Parametric Monotonicity
Filomena Garcia Optimization
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Optimization Problems in Rn
Optimization Filomena Garcia Optimization
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
An optimization problem in Rn is one where the values of a given function f : Rn → R are to be maximized or minimized over a given set D ⊂ Rn . The function f is called objective function and the set D is called the constraint set. We denote the optimization problem as: max {f (x) |x ∈ D} A solution to the problem is a point x ∈ D such that f (x) ≥ f (y ) for all y ∈ D. We call f (D) the set of attainable values of f in D.
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Filomena Garcia
Optimization
Optimization Filomena Garcia Optimization
Optimization Problems in Rn
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
Mathematical Economics - Part I Optimization
Filomena Garcia
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Fall 2009
Filomena Garcia
Optimization
Optimization Filomena Garcia Optimization
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
1 Optimization in Rn
Optimization Problems in Rn Optimization Problems in Parametric Form Optimization Problems: Some Examples The objectives of Optimization Theory
2 Existence of Solutions 3 Unconstrained Optima 4 Equality Constraints 5 Inequality Constraints 6 Convex Structures in Optimization Theory 7 Quasiconvexity in Optimization 8 Parametric Continuity: The Maximum Theorem 9 Supermodularity and Parametric Monotonicity
Filomena Garcia Optimization
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Optimization Problems in Rn
Optimization Filomena Garcia Optimization
Optimization Problems in Rn Parametric Form Examples The objectives of Optimization Theory
An optimization problem in Rn is one where the values of a given function f : Rn → R are to be maximized or minimized over a given set D ⊂ Rn . The function f is called objective function and the set D is called the constraint set. We denote the optimization problem as: max {f (x) |x ∈ D} A solution to the problem is a point x ∈ D such that f (x) ≥ f (y ) for all y ∈ D. We call f (D) the set of attainable values of f in D.
Existence of Solutions Unconstrained Optima Equality Constraints Inequality Constraints Convex Structures in Optimization Theory Quasiconvexity
Filomena Garcia
Optimization
Optimization Filomena Garcia Optimization
Optimization Problems in Rn