6.253 Convex Analysis and Optimization, Spring 2004
Convex Analysis and Optimization
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6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject.
affine hulls, recession cones, global minima, local minima, optimal solutions, hyper planes, minimax theory, polyhedral convexity, polyhedral cones, polyhedral sets, convex analysis, optimization, convexity, Lagrange multipliers, duality, continuous optimization, saddle point theory, linear algebra, real analysis, convex sets, convex functions, extreme points, subgradients, constrained optimization, directional derivatives, subdifferentials, conical approximations, Lagrange multipliers, Fritz John optimality, Exact penalty functions, conjugate duality, conjugate functions, Fenchel duality, exact penalty functions, dual computational methods
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Basis descent methods for convex essentially smooth optimization with applications to quadratic/entropy optimization and resource allocation Tseng, Paul.; Massachusetts Institute of Technology. Laboratory for Information and Decision Systems. (Massachusetts Institute of Technology, Laboratory for Information and Decision Systems], 1989)