Convex optimization of functions

  • Can you maximize a convex function?

    The maximum of a convex function over a compact convex set is attained at one of the extreme points of the convex set (can you prove this?). and (b,0,0,⋯,0),(0,b,0,⋯,0),⋯(0,⋯,0,b).
    It is easy to check that the maximum occurs at any one of the latter set of extreme points.
    The case when a=b is simpler..

  • What is the function of a convex function?

    A convex function is a continuous function whose value at the midpoint of every interval in its domain does not exceed the arithmetic mean of its values at the ends of the interval..

  • The function f is convex on the interval I iff for every a, b ∈ I, the line segment between the points (a, f(a)) and (b, f(b)) is always above or on the curve f.
    Analogously, f is concave iff the line segment always lies below or on the curve.

Categories

Opposite of optimizing
Convex optimization permutation
Convex optimization for electrical engineering
Convex optimization
Convex optimization by stephen boyd and lieven vandenberghe
Bandit convex optimization towards tight bounds
Optimization under constraints
Convex optimization and applications
Convex optimization and concave
Convex optimization and geometry
Convex optimization and dual problem
Convex optimization and linear algebra
Convex optimization and cost function
Convex optimization and tensors
Convex optimization and derivatives
Convex optimization and operation research
Large-scale convex optimization via monotone operators
Non convex optimization
Convex optimization-based beamforming
Smoothed online convex optimization based on discounted-normal-predictor