
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
September 19th, 2017, 05:14 AM  #1 
Senior Member Joined: Dec 2011 Posts: 112 Thanks: 2  Convexity of nonlinear problem
Problem in English: ''Find out if the following nonlinear optimization problem is convex.'' Tried solving det(Hlambda*I)=0 and see for which interval x will give positive lambda roots. Not sure how I'm supposed to approach this.. Tried using pqformula but got wrong roots for lambda, or try using Sylvester's criterion. Last edited by skipjack; September 19th, 2017 at 11:09 AM. 
September 20th, 2017, 05:00 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,731 Thanks: 707 
$\displaystyle x_1^2+ x_2^2= 2$ is a circle with center at (0, 0) and radius $\displaystyle \sqrt{2}$ so $\displaystyle x_1^2+ x_2^2\le 2$ is that circle and its interior, a convex set. Completing the square in $\displaystyle 4x_1^2+ 3x_1x_2+ x_2^2\le 4$ gives $\displaystyle 4(x_1+ \frac{3}{8}x_2)^2+ \frac{25}{64}x_2^3\le 4$, an ellipse with its axes at an angle to the coordinate axes and its interior, also a convex set. The intersection of two convex sets is a convex set.


Tags 
convexity, nonlinear, problem 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
proving convexity  walter r  Linear Algebra  1  July 20th, 2013 04:53 PM 
Proof  convexity  Vasily  Applied Math  1  August 10th, 2012 02:12 AM 
Convexity  Vasily  Applied Math  2  June 24th, 2012 02:37 AM 
convexity proofs  alexs87  Real Analysis  0  July 10th, 2008 11:46 AM 
convexity  ^e^  Real Analysis  5  November 5th, 2007 07:38 AM 