Piecewise convex optimization problem

  • Can a piecewise linear function be convex?

    In one of his lectures on convex functions, Stephen Boyd claimed piecewise linear functions are convex because a piecewise linear function can be thought of as pointwise maximum of a set of affine functions..

  • How can we solve a convex optimization problem?

    For a piecewise linear quadratic (PLQ) function, convexity can be characterized with a linear number of constraints with respect to the number of edges of the partition defining the domain.
    The number of constraints in .

    1. D is in fact linear with respect to the number of vertices in the domain

  • How do you show a piecewise function is convex?

    Unconstrained convex optimization can be easily solved with gradient descent (a special case of steepest descent) or Newton's method, combined with line search for an appropriate step size; these can be mathematically proven to converge quickly, especially the latter method..

  • What is the convexity of a piecewise linear function?

    Gradient descent is a popular alternative because it is simple and it gives some kind of meaningful result for both convex and nonconvex optimization.
    It tries to improve the function value by moving in a direction related to the gradient (i.e., the first derivative)..

  • Gradient descent is a popular alternative because it is simple and it gives some kind of meaningful result for both convex and nonconvex optimization.
    It tries to improve the function value by moving in a direction related to the gradient (i.e., the first derivative).
Jul 5, 2021Nonconvex optimization problems can have a large number of local minima which makes the problem of finding the global solution difficult.

Scholarly articles for piecewise convex optimization problem

scholar.google.com › citationsPiecewise-convex maximization problems
TsevendorjCited by 41Piecewise-convex maximization problems: algorithm …
FortinCited by 15… piecewise linear structure in convex optimization
JohnsonCited by 16
Jul 5, 2021Nonconvex optimization problems can have a large number of local minima which makes the problem of finding the global solution difficult.

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