Convex analysis. Convex sets. -- Convex functions and generalizations. -- Optimality conditions and duality. -- The Fritz John and Karush-Kuhn-tucker optimality conditions. -- Constraint qualifications. -- Lagrangian duality and saddle point optimality conditions. -- The concept of an algorithm. -- Unconstrained optimization. -- Penalty and barrier functions. -- Methods of feasible directions. -- Linear complementary problem, and quadratic, separable, fractional, and geometric programming.
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