No abstract

The African continent currently faces severe political and economic crises. Massive debts, unpopular structural adjustment programmes (S.A.P.s), spiralling population growth, democratisation, and régime transformation are all testing national cohesion. Externally, the rapidly changing global environment, marked by the demise of the cold war and the continuing difficulties being experienced in Europe and the Middle East, also provides immense challenges to African policy-makers.

Optimization techniques are at the core of data science, including data analysis and machine learning. An understanding of basic optimization techniques and their fundamental properties provides important grounding for students, researchers, and practitioners in these areas. This text covers the fundamentals of optimization algorithms in a compact, self-contained way, focusing on the techniques most relevant to data science. An introductory chapter demonstrates that many standard problems in data science can be formulated as optimization problems. Next, many fundamental methods in optimization are described and analyzed, including: gradient and accelerated gradient methods for unconstrained optimization of smooth (especially convex) functions; the stochastic gradient method, a workhorse algorithm in machine learning; the coordinate descent approach; several key algorithms for constrained optimization problems; algorithms for minimizing nonsmooth functions arising in data science; foundations of the analysis of nonsmooth functions and optimization duality; and the back-propagation approach, relevant to neural networks.

No abstract

No abstract