Exact multiplicity of positive solutions for concave—convex and convex—concave nonlinearities Documents. For each s, the function f sx is convex in x. Boyd EEa Homework 6 solutions 8. These functions are often used in economics to model the benefit or utility of somequantity of goods or money. If we repeat the same analysis for the second function, we see that it could be concave and therefore it could be quasiconcave. Boyd EEa Homework 1 solutions 2. Eea homework 6 solutions.
It is also not convex, for the following reason. We show that the function is quasiconcave. EEa Homework 2 solutions. This defines a convex set. Eea homework 6 solutions. Since this is negative for all x, we conclude that u is strictly concave. EEa, Winter Prof.
Boyd EEa Homework 6 solutions 6. Boyd EEa Homework 2 solutions 2.
Homework 2 Solutions Documents. Boyd EEa Homework 6 solutions. Eea homework 6 solutions.
Show that its running average Fdefined as. Solutions for Homework Assignment 2 Documents. This iseasily verified by working out the Hessian:.
EE364: Convex Optimization with Engineering Applications
EEa Homework 8 solutions. Therefore, f is not convex orconcave. The minimum fuel optimal control problem is equivalent to the LP.
See also figure 3. In addition it is not quasiconvex in general. Toshow concavity, we examine the second derivative:. We show that the function is quasiconcave. A convex ora concave function is always continuous on the relative interior of its domain. The sublevel and the superlevel sets of quartile x are convex seeproblem 2.
Homework 2 Solutions – 2 Solutions Author: When is theepigraph of a function a convex cone? It is not quasiconcave or concave. Boyd EEa Homework 6 solutions 8. Clearly along this line segment, the function is not convex. If we repeat the same analysis for the second function, we see that it could be concave and therefore it could be quasiconcave. Since this is negative for all x, we conclude that u is strictly concave. It is quasiconvex and quasiconcave i.
EE Convex Optimization & Applications
It is definitely not concave or quasiconcave because the superlevel sets arenot convex. Apr 30, Optimization, Spring Show that the following problem is quasiconvex: It is quasiconcave, since its superlevel sets.
For each s, the function f sx is convex in x. This is readily shown by induction from the definition of convex set. EEa Homework 7 solutions Documents. In other words, concavity models the effect of satiation.
EEa Homework 2 solutions – see. Repeatfor the level curves shown below.