- Why is a² + b² ≥ 2ab ?
- A remark on the divergence theorem
- The Cauchy-Schwarz inequality and the Lagrange identity
- On the existence of a metric compatible with a given connection
- A curious identity on the median triangle
- 27 lines on a smooth cubic surface
- Weighted Hsiung-Minkowski formulas and rigidity of umbilic hypersurfaces
- The discrete Gauss-Bonnet theorem
- Why a vector field rotates about its curl?
- A functional inequality on the boundary of static manifolds
tong cheung yu on On the existence of a metric c… Marco Barchiesi on Simple curves with a positive… tong cheung yu on Toric perspective 1 lamwk on Why is a² + b² ≥ 2ab ? Maurice OReilly on Spherical cosine law KKK on Sobolev and Isoperimetric… Anonymous on Sobolev and Isoperimetric… tong cheung yu on On the existence of a metric c… Anonymous on Closed subspaces of a reflexiv… KKK on A curious identity on the medi…
- Algebraic geometry
- Applied mathematics
- Complex analysis
- Differential equations
- Discrete Mathematics
- Dynamical system
- Fourier analysis
- Functional analysis
- General Relativity
- Group theory
- Linear Algebra
- Number Theory
- Operator Theory
- Potential theory
- Set Theory
- Martingale Theory II: Conditional expectation
- Complex analysis - Problem solving strategies.
- Do join us!
- Mean value properties for harmonic functions on Riemannian manifolds
- A note on Obata's theorem
- Mathematics behind JPEG
- Understanding Lagrange multipliers (1)
- The Brunn-Minkowski inequality and the isoperimetric inequality
- Why does a mirror reverse left and right, but not top and bottom?
Category Archives: Optimization
It has been a while since the last post. Let us recall what we have done. We study the unconstrained polynomial optimization problem () where is a real polynomial. This problem is equivalent to () … Continue reading
In this post we shall give another proof of the famous AM-GM-HM inequality: If are positive real numbers, then AM GM HM, precisely .
In this article we shall describe something called Gram-matrix method which can decompose a polynomial into sum of squares. The notation means is a square symmetric positive semidefinite matrix. Proposition 1. Let , be a polynomial … Continue reading
This post aims at proving a standard result in quadratic programming called S-Lemma. The use of this result will be obvious in a future post. We begin with a lemma. Lemma 1. Let be two … Continue reading
(Nov 28, 2013) A (constrained) polynomial minimization problem is in the form () subject to where are polynomials in with real coefficients. If and , then the above problem becomes , an unconstrained polynomial minimization problem. … Continue reading
(Sept 17, 2013) Our little plan is to write a series of posts discussing a sequence of optimization problems. Before we dive into them, it is cool to learn a rigorous treatment of standard complexity notions P, NP, NP-hard and … Continue reading
This is my first time trying to upload my notes here. If the Acrobat Reader does not show all words, please close the file and open the file again. Foundations of Optimization (5 July 2011)