Abstract
It is shown that the following classes of functionsf, each defined on some subsetD of a fixed Hausdorff topological vector spaceE, are closed under the binary operation of infimal convolution: (a) the class of functionsf:D→[−∞, ∞) having connectedstrict lower level sets; (b) the class of functionsf:D→ℝ having compact connected lower level sets; and (c) the class of functionsf:D→ℝ having compact lower level sets and for which every local minimizer is global. In (a),E need not be Hausdorff; while in (a) and (b), the word “connected” may be replaced by the word “path-connected.”
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Communicated by M. A. Avriel
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Martin, D.H. Some function classes closed under infimal convolution. J Optim Theory Appl 25, 579–584 (1978). https://doi.org/10.1007/BF00933523
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DOI: https://doi.org/10.1007/BF00933523