This thesis presents a new algorithm for Mixed Integer NonLinear Programming, inspi- red by the multiplicativeweightsupdate frame- work and relying on a new class of reformulations, called the pointwise reformulatio...
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This thesis presents a new algorithm for Mixed Integer NonLinear Programming, inspi- red by the multiplicativeweightsupdate frame- work and relying on a new class of reformulations, called the pointwise reformulations. Mixed Integer NonLinear Programming is a hard and fascinating topic in Mathematical Optimiza- tion both from a theoretical and a computational viewpoint. Many real-world problems can be cast this general scheme and, usually, are quite challen- ging in terms of efficiency and solution accuracy with respect to the solving procedures. The thesis is divided in three main parts: a fore- word consisting in Chapter 1, a theoretical founda- tion of the new algorithm in Chapter 2, and the ap- plication of this new methodology to two real-world optimization problems, namely the Mean-Variance Portfolio Selection in Chapter 3, and the Multiple NonLinear Separable Knapsack Problem in Chap- ter 4. Conclusions and open questions are drawn in Chapter 5.
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