Partly Convex and Convex-Monotonic Optimization Problems
A class of nonconvex optimization problems is studied that exhibits partial convexity combined with partial monotonicity. To exploit this particular hybrid structure a natural approach is to use a branch and bound scheme with branching performed on the nonconvex variables and bounds computed by lagrangian or convex relaxation. We discuss conditions that guarantee convergence of such branch and bound algorithms. Incidentally, several incorrect results in the recent literature on related subjects are reviewed.
Key wordsNonconvex optimization hybrid convex-monotonic optimization partly convex programming branch and bound method lagrangian relaxation dual bound consistent bound
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