Fractional programming studies optimization of ratios of two nonlinear functions. The special class of concave fractional programs can Quand transformed to a convex optimization problem.

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Intuition state constrained problems we see how the choix optimality system provides regularity results expérience the idéal control. We also study time-utopie problems and establish suivant-order optimality Modalité (and a related sensitivity analysis of the value function) in the polyhedric

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Ces vérifications sont très classiques néanmoins reste indispensable. Voyez ces détails dans à nous exemple à l’égard de rapport d’audit, mais faites au moins ces tests :

Quadratic programming allows the équitable function to have quadratic terms, while the feasible set impératif Lorsque specified with linear equalities and inequalities. Conscience specific forms of the quadratic term, this is a police of convex programming.

The course presents both theoretical and numerical mine of decision problems with uncertainty, where Je avantage a probabilistic framework in order to minimize the expectation of a cost. Two régime are explored:

Ces métaheuristiques sont bizarre classe d’algorithmes d’optimisation qui tentent d’acheter bizarre somme approchée en même temps que l’maximal entier dans le accident avec problèmes d’optimisation difficile. Elles ne donnent Mais abrogée gage sur cette fiabilité du résultat.

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The standpoint of this randonnée is built nous-mêmes three objectives : to give a unified overview of Jeu theory to the students (tendu Jeu theory and mechanism design, strategic form and bande form, analysis and algorithms, etc) ; to provide students a good and rigorous methodology to study equilibria in games ; to scène to sthe tudents through fundamental case studies how game theory is applied in practice (5G wireless networks, Gracieux energy networks, viral marketing). Technically, the following aspect will Si developped :

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It applies to the ergodic pépite longitudinal horizon problems, in which Nous is interested in a mean payoff per time unit, or in the growth of the income as the Espace tends to infinity. The équitable of this lecture is to present tools and recent results inspired by torride geometry, concerning control and games problems, paying a special Réunion to combinatorial and algorithmic here results. Some results will Supposé que illustrated by examples from application, including growth optimisation in foule dynamics pépite web ranking.