The Multiplicative Weights Update Algorithm for Mixed Integer NonLinear Programming : Theory, Applications, and Limitations

Abstract : This thesis presents a new algorithm for Mixed Integer NonLinear Programming, inspired by the Multiplicative Weights Update framework and relying on a new class of reformulations, called the pointwise reformulations.Mixed Integer NonLinear Programming is a hard and fascinating topic in Mathematical Optimization both from a theoretical and a computational viewpoint. Many real-word problems can be cast this general scheme and, usually, are quite challenging in terms of efficiency and solution accuracy with respect to the solving procedures.The thesis is divided in three main parts: a foreword consisting in Chapter 1, a theoretical foundation of the new algorithm in Chapter 2, and the application 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 Chapter 4. Conclusions and open questions are drawn in Chapter 5.
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Luca Mencarelli. The Multiplicative Weights Update Algorithm for Mixed Integer NonLinear Programming : Theory, Applications, and Limitations. Optimization and Control [math.OC]. Université Paris-Saclay, 2017. English. ⟨NNT : 2017SACLX099⟩. ⟨tel-01784066⟩

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