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Category Archives: Optimization
Polynomial Optimization 3: Why do we need generalize?
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
Posted in Algebra, Applied mathematics, Optimization
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AMGMHM Inequality: A Statistical Point of View
In this post we shall give another proof of the famous AMGMHM inequality: If are positive real numbers, then AM GM HM, precisely .
Posted in Applied mathematics, Calculus, Optimization, Statistics
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Polynomial Optimization 2: SOS and SDP
In this article we shall describe something called Grammatrix 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
Posted in Algebra, Applied mathematics, Optimization
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SLemma
This post aims at proving a standard result in quadratic programming called SLemma. The use of this result will be obvious in a future post. We begin with a lemma. Lemma 1. Let be two … Continue reading
Posted in Applied mathematics, Linear Algebra, Optimization
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Polynomial Optimization 1: Motivation
(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
Posted in Algebra, Applied mathematics, Optimization
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The World of Complexity
(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, NPhard and … Continue reading
Posted in Applied mathematics, Optimization
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Notes on Optimization
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)