Convex optimization basics

  • What is convex function optimization?

    A convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing.
    Linear functions are convex, so linear programming problems are convex problems..

  • 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.
  • An intuitive definition: a function is said to be convex at an interval if, for all pairs of points on the graph, the line segment that connects these two points passes above the curve. curve.
    A convex function has an increasing first derivative, making it appear to bend upwards.
May 6, 2020The basics of convex optimization. Duality, linear programs, etc. Princeton COS 302, Lecture 22.
Duration: 21:32
Posted: May 6, 2020
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets).

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