Lecture Notes on Constraint Convex Optimization
نویسنده
چکیده
where f(w) is called the objective function, gi(w) the inequality constraints, and hi(w) the equality constraints. The optimal value f(w∗) of the objective function is called the value of the optimization problem. The feasible region is defined by all w ∈M for which ∀i = 1, . . . , k : gi(w) ≤ 0 ∧ ∀j = 1, . . . ,m : hj(w). If for an inequality constraint gi(w) = 0, then the constraint gi is called active, if gi(w) < 0, then gi is called inactive. Because maximizing a function f(w) for w ∈ M corresponds to minimizing −f(w) for w ∈M , we just consider minimization in the following.
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Linear Programming Notes
These notes summarize the central definitions and results of the theory of linear programming, as taught by David Williamson in ORIE 6300 at Cornell University in the fall of 2014. Proofs and discussion are mostly omitted. These notes also draw on Convex Optimization by Stephen Boyd and Lieven Vandenberghe, and on Stephen Boyd’s notes on ellipsoid methods. Prof. Williamson’s full lecture notes ...
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