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Foundations of optimization Prove the following statements: Everyintersectionofapolytopewithanaffinesubspaceisapolytope.Thus,acrosssectionofapolytopeisapolytope. Everyintersectionofapolytopewithapolyhedronisapolytope. TheMinkowskisumoftwopolytopesisapolytope Anaffineimageofapolytopeisapolytope. A projection of a polytope onto an affine subspace is a polytope.

Foundations of optimization

Prove the following statements:

  1. Everyintersectionofapolytopewithanaffinesubspaceisapolytope.Thus,acrosssectionofapolytopeisapolytope.
  2. Everyintersectionofapolytopewithapolyhedronisapolytope.
  3. TheMinkowskisumoftwopolytopesisapolytope
  4. Anaffineimageofapolytopeisapolytope.
  5. A projection of a polytope onto an affine subspace is a polytope.

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