Theory official Flashcards
(35 cards)
Single objective optimization / scalar optimization: mathematical definition
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Definition of global minimum, local minimum, convexity
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Optimality conditions (constrained+unconstrained): KKT conditions
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Non linear optimization: is it possible to guarantee a global optimum? Why? List the 2 main heuristic rules on which the algorithms are based. What is the general search procedure for optimization problems?
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5 properties of a good algorithm
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Grid and random methods, Pattern search and Simplex method
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Basic descend methods
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Penalty methods
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MOP: mathematical definition of the Pareto optimal solution and meaning. Local vs global Pareto optimal solution.
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Pareto optimal necessary condition. Ideal vs Nadir solution
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Low discrepancy sequences. Definition of uniformity and discrepancy
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Feasibility and boundedness
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Scalarization techniques
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Lagrange multipliers
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John Fritz optimal condition
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Discrete programming
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Genetic algorithms: introduction and explanation. Binary coding representation for discrete, continuous and multi design variables. Description of the process in detail
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Holland theorem: schema properties and number of elements with a schema at a certain generation
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Constraints in GAs
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Termination conditions for GA and no free lunch theorem
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Multiobjective optimization with GA. Main advantages. How to assign the fitness and how to guarantee even distribution?
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Global sensitivity analysis: Pearson and Spearman indexes. Scatterplots. Linear regression
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Global approximation: least square
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Machine learning: introduction to neural networks. Structure of the artificial neural network, example of a multi layer feed forward network and activation functions.
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