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The polyhedral method treats each loop iteration within nested loops as lattice points inside mathematical objects called polyhedra, performs affine transformations or more general non-affine transformations such as tiling on the polytopes, and then converts the transformed polytopes into equivalent, but optimized (depending on targeted ...
For example, the feasible set defined by the constraint set {x ≥ 0, y ≥ 0} is unbounded because in some directions there is no limit on how far one can go and still be in the feasible region. In contrast, the feasible set formed by the constraint set { x ≥ 0, y ≥ 0, x + 2 y ≤ 4} is bounded because the extent of movement in any ...
Loop unrolling, also known as loop unwinding, is a loop transformation technique that attempts to optimize a program's execution speed at the expense of its binary size, which is an approach known as space–time tradeoff. The transformation can be undertaken manually by the programmer or by an optimizing compiler.
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements and objective are represented by linear relationships.
Matrix chain multiplication is a well-known example that demonstrates utility of dynamic programming. For example, engineering applications often have to multiply a chain of matrices. It is not surprising to find matrices of large dimensions, for example 100×100. Therefore, our task is to multiply matrices ,,....
Some engineering applications of SOCP include filter design, antenna array weight design, truss design, and grasping force optimization in robotics. [4] Applications in quantitative finance include portfolio optimization ; some market impact constraints, because they are not linear, cannot be solved by quadratic programming but can be ...
A causal loop diagram of growth and underinvestment The growth and underinvestment archetype is one of the common system archetype patterns defined as part of the system dynamics discipline. System dynamics is an approach which strives to understand, describe and optimize nonlinear behaviors of complex systems over time, using tools such as ...
Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously.