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Properties of minimizers and maximizers of functions rely intimately on a wealth of tech- niques from mathematical analysis, including tools from calculus and its generalizations, topological notions, and more geometric ideas. The the- ory underlying current computational optimization techniques grows ever more sophisticated — duality-based algorithms, interior point methods, and control-theoretic applications are typical examples.
The powerful and elegant language of convex analysis unifies much of this theory. Hence our aim of writing a concise, accessible account of convex analysis and its applications and extensions, for a broad audience.
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Assignments will consist of theoretical problems requiring mathematical proofs and computational problems involving algorithm implementation and problem-solving on computer. Theoretical problems are generally ungraded with their solutions available in the Solution Manuals. Computer problems will be graded.
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While students can discuss about the assigned problems with others, they must write out the solutions and programs individually by themselves no sharing of identical solutions or copying codes from each others. Exams Two exams are planned: a midterm in-class and a final take-home. A part of the final may include problem-solving on computer.