Convex optimization cambridge university press

  • Unconstrained convex optimization can be easily solved with gradient descent (a special case of steepest descent) or Newton's method, combined with line search for an appropriate step size; these can be mathematically proven to converge quickly, especially the latter method.

Is x r2 a convex optimization problem?

Consider the example with x∈ R2, minimize f 0(x) = x2 1+x2 2 subject to f 1(x) = x 1/(1+x2 2) ≤ 0 h 1(x) = (x 1+x 2)2= 0, (4

17) which is in the standard form (4

1)

This problem is not a convex optimization problem in standard form since the equality constraint function h 1is not affine, and


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