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Lipschitzian Optimization and Systems of Equations
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accumulation point affine function argmin assume basic optimal solution BB procedure bisection bounding operation branch and bound compute con(Q concave function concave minimization problem concave programming concavity cut cone conical algorithm consider construct contains convergence convex envelope convex function convex hull convex programming convex set Corollary d.c. programming defined deletion denote edge extreme directions facet feasible point feasible set follows function f global optimal solution global optimization problems halfline halfspace hence Horst hyperplane implies inequality infinite nested sequence int G intersection iteration Lemma linear program Lipschitz constant Lipschitzian lower bound LRCP matrix minimize f(x nondegenerate objective function obtained optimal value Otherwise outer approximation method partition elements partition sets polyhedron polytope programming problem Proof Proposition quadratic relaxed problem satisfying Section simplex simplices Step subdivision process subproblem supporting hyperplane Theorem Thoai vector vertex set vertices