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CrossDual on The Golden Optimum Solutions
"... This paper owes its origin to two simple minimization problems. One is a shortest distance problem on the plane. The other is a ratio minimization problem over the unit interval. We associates each of two minimization problems with a counterpart “maximization problem. Thus we consider two couples o ..."
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quadratic constraint. An optimum solution – optimum point and optimum value – is called Golden if both the slope and the optimum value constitute the Golden ratio. We show two interesting features. One is the Golden optimum solution. All six problems have the Golden optimum slutions. The other is a cross
OPTIMUM SOLUTIONS FOR GROWERFINISHER PIGS
"... Dynamic integrated models, such as Watson®, are available and being used to improve performance and profitability of finishing pigs by enhancing the decisionmaking process. One of the main purposes of an integrated management approach is to bring together the complex interactions between the animal ..."
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of these changes; and therefore, 3) the optimum nutritional and/or financial strategy. It is important to note that optimum solutions are farmspecific and no one solution fits all because of the inherent differences in production characteristics on each farm (e.g health status, genetics, housing, ingredient
The Advantages of Evolutionary Computation
, 1997
"... Evolutionary computation is becoming common in the solution of difficult, realworld problems in industry, medicine, and defense. This paper reviews some of the practical advantages to using evolutionary algorithms as compared with classic methods of optimization or artificial intelligence. Specific ..."
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Cited by 536 (6 self)
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advantages include the flexibility of the procedures, as well as the ability to selfadapt the search for optimum solutions on the fly. As desktop computers increase in speed, the application of evolutionary algorithms will become routine. 1 Introduction Darwinian evolution is intrinsically a robust search
Obtaining exact solution from a near optimum solution for convex QP
"... Consider a convex quadratic program of size L involving m inequality constraints and possibly some equality constraints in n variables. Given a feasible solution whose objective value is within 2 \Gamma2L of the optimum objective value, we discuss a technique that finds a true optimum solution in ..."
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Consider a convex quadratic program of size L involving m inequality constraints and possibly some equality constraints in n variables. Given a feasible solution whose objective value is within 2 \Gamma2L of the optimum objective value, we discuss a technique that finds a true optimum solution
For Most Large Underdetermined Systems of Linear Equations the Minimal ℓ1norm Solution is also the Sparsest Solution
 Comm. Pure Appl. Math
, 2004
"... We consider linear equations y = Φα where y is a given vector in R n, Φ is a given n by m matrix with n < m ≤ An, and we wish to solve for α ∈ R m. We suppose that the columns of Φ are normalized to unit ℓ 2 norm 1 and we place uniform measure on such Φ. We prove the existence of ρ = ρ(A) so that ..."
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Cited by 560 (10 self)
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that for large n, and for all Φ’s except a negligible fraction, the following property holds: For every y having a representation y = Φα0 by a coefficient vector α0 ∈ R m with fewer than ρ · n nonzeros, the solution α1 of the ℓ 1 minimization problem min �x�1 subject to Φα = y is unique and equal to α0
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 973 (4 self)
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the least
Finding globally optimum solutions in antenna optimization problems
 IEEE International Symposium on Antennas and Propagation
, 2010
"... During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techn ..."
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Cited by 3 (2 self)
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During the last decade, the unprecedented increase in the affordable computational power has strongly supported the development of optimization techniques for designing antennas. Among these techniques, genetic algorithm [1] and particle swarm optimization [2] could be mentioned. Most of these techniques use physical dimensions of an antenna
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
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Cited by 1772 (10 self)
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How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LSA), is presented and used to successfully simulate such learning and several other psycholinguistic phenomena. By inducing global knowledge indirectly from local cooccurrence data in a large body of representative text, LSA acquired knowledge about the full vocabulary of English at a comparable rate to schoolchildren. LSA uses no prior linguistic or perceptual similarity knowledge; it is based solely on a general mathematical learning method that achieves powerful inductive effects by extracting the right number of dimensions (e.g., 300) to represent objects and contexts. Relations to other theories, phenomena, and problems are sketched.
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