...problem is a convex programming problem, that...
...if f(x) is convex g(x) are concave...
...concave (form a convex set) Another possibility...
...f is both convex and strictly convex....
...convex and strictly convex. * x T...
...f is both convex and strictly convex....
...convex and strictly convex. Problem 4.16 2...
...def. 2()x21xx2224 strictly convex 222 fxxx 123...
...3 002 strictly convex xx12 fee x...
...0 e strictly convex in the finite...
...f is strictly convex over finite values...
...x2, and thus convex. 12 Problem 4.18...
...LR function is convex. (b) x1x22fxf0fx, 0....
...and f is convex for 0 <...
...fxLRxf())22 f is convex for 0 <...
...1212). f is convex. 13 Problem 4.19...
...region is thus convex. It is also...
...constraints form a convex region. Problem 4.21...
...is concave and convex. 100 14 Thus,...
...the region is convex. That it is...
...the region is convex, all the constraints...
...concave (it is convex). 16 Answer: No....
...the term is convex. The Hessian of...
...a sum of convex terms is the...
...of (x) is convex. For example: 22...
...if f(x) is convex and gx1()0 is...
...and gx1()0 is convex. The Hessian matrix...
...Hx() is f(x) convex? 200400 223 x1x2xx12...
...so f(x) is convex xx12 0 xx12...
...g < 0 convex? The Hessian matrix...
...that g(x) is convex The xi 0...
...xi 0 are convex functions. Consequently, the...
...problem is a convex programming problem for...
...function asymptodically is convex. 18 Problem 4.27...
...do form a convex region (they all...
...and form a convex region. Problem 4.31...
...f is not convex over this entire...
...f () is convex (a)x x1x2xx12 300...
...that g(x) is convex 22 concave Also...
...Also 0xi are convex but the constraint...
...is not a convex region because g()0x...
...region to be convex. The following figure...
...g()1x is not convex. In P. 4.26...
...is not a convex function for all...
...f is not convex at P =...
...is therefore, not convex in some small...
...region is not convex because the line...
..."()0, f is convex. Repeat the above...
...function is strictly convex at (0.654, -0.916)...