Optimal convex decompositions

  • Is the classic convex decomposition optimal for bound preserving schemes in multiple dimensions?

    In this work, we find, in the multidimensional cases, that the classic decomposition is generally not optimal for the spaces, i.e. the multivariate polynomial spaces of total degree up to k..

  • What is a convex partition of a polygon?

    A convex partition by diagonals of a polygon �� is a decomposition of �� into convex polygons obtained by only introducing diagonals.
    Page 34 Convex Partitions Definition: A convex partition by segments of a polygon �� is a decomposition of �� into convex polygons obtained by introducing arbitrary segments..

  • What is fast approximate convex decomposition?

    In Fast Approximate Convex Decomposition (FACD), the decomposition is improved by selection of multiple segmentation boundaries for decomposition from a set of possible segmentation boundaries..

  • What is the definition of a convex shape?

    A convex shape is the opposite of a concave shape.
    It curves outward, and its middle is thicker than its edges.
    If you take a football or a rugby ball and place it as if you're about to kick it, you'll see that it has a convex shape—its ends are pointy, and it has a thick middle..

A decomposition is said to be convez if all its polygons are convex. We define an optimal convez decomposition of P, or OCD for short, as any convex decomposition of minimum cardinality.
There are several challenges faced when extending ACD to polyhedra.One operation that we use to address some of th…
Benders decomposition is a technique in mathematical programming that allows the solution of very large linear programming problems that have a special block structure.
This block structure often occurs in applications such as stochastic programming as the uncertainty is usually represented with scenarios.
The technique is named after Jacques F.
Benders.

Categories

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Non-convex optimization with neural networks