- #1
nacho-man
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Hi everyone,
I will be taking a summer course on Optimisation - AMSI Summer School
and was wondering if you could recommend any books.
The course outline is:
Week 1: Introduction to Optimization problems: classification and examples. Elements of convex analysis: convex sets and convex functions, differentiability properties of convex functions, one-sided directional derivatives, epigraphs and level sets.
Week 2: Separation results for convex sets, topological properties ofconvex sets, subgradients of convex functions. Existence of solutions of optimization problems: boundedness and coerciveness. First and second order optimality conditions: Unconstrained case. Constrained case: Equality and inequality constraints for differentiable problems.
Week 3: Sensitivity analysis for unconstrained optimization. Optimality conditions for convex (non-differentiable) problems. Maximum of a
convex function.
Week 4: Methods for Unconstrained Optimization: Newton method and its variants, and their convergence analysis. Cauchy and Armijo variants of steepest descent and convergence analysis of descent type methods. Methods for Constrained Optimization: Penalty Methods, Exact penalty methods and Lagrange multipliers, Barrier methodsFurthermore has anyone done optimisation? How would you rate it in terms of difficult compared to say, time series analysis or complex analysis?
I am coming with a robust background in multivariable calc and linear algebra.
I will be taking a summer course on Optimisation - AMSI Summer School
and was wondering if you could recommend any books.
The course outline is:
Week 1: Introduction to Optimization problems: classification and examples. Elements of convex analysis: convex sets and convex functions, differentiability properties of convex functions, one-sided directional derivatives, epigraphs and level sets.
Week 2: Separation results for convex sets, topological properties ofconvex sets, subgradients of convex functions. Existence of solutions of optimization problems: boundedness and coerciveness. First and second order optimality conditions: Unconstrained case. Constrained case: Equality and inequality constraints for differentiable problems.
Week 3: Sensitivity analysis for unconstrained optimization. Optimality conditions for convex (non-differentiable) problems. Maximum of a
convex function.
Week 4: Methods for Unconstrained Optimization: Newton method and its variants, and their convergence analysis. Cauchy and Armijo variants of steepest descent and convergence analysis of descent type methods. Methods for Constrained Optimization: Penalty Methods, Exact penalty methods and Lagrange multipliers, Barrier methodsFurthermore has anyone done optimisation? How would you rate it in terms of difficult compared to say, time series analysis or complex analysis?
I am coming with a robust background in multivariable calc and linear algebra.