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Let A_n be the set of all sequences that contain all sequences {a_k}_(k=0)^n where a_0=1 and all other a_i=+/-1, and define c_k=sum_(j=0)^(n-k)a_ja_(j+k). Then the merit ...

A branch of mathematics which encompasses many diverse areas of minimization and optimization. Optimization theory is the more modern term for operations research. ...

Bubbles can meet only at angles of 120 degrees (for three bubbles) and cos^(-1)(-1/3) approx 109 degrees28^'16^('') (for four bubbles), where cos^(-1)(-1/3) is the ...

Define f(x_1,x_2,...,x_n) with x_i positive as f(x_1,x_2,...,x_n)=sum_(i=1)^nx_i+sum_(1<=i<=k<=n)product_(j=i)^k1/(x_j). (1) Then minf=3n-C+o(1) (2) as n increases, where the ...

Branch and bound algorithms are a variety of adaptive partition strategies have been proposed to solve global optimization models. These are based upon partition, sampling, ...

Differential evolution is a stochastic parallel direct search evolution strategy optimization method that is fairly fast and reasonably robust. Differential evolution is ...

A direct search method of optimization that works moderately well for stochastic problems. It is based on evaluating a function at the vertices of a simplex, then iteratively ...

Heule graphs are a set of unit-distance graphs with chromatic number five derived by Marijn Heule in April 2018 to July 2918 from the 1581-vertex de Grey Graph (Heule 2018). ...

The largest value of a set, function, etc. The maximum value of a set of elements A={a_i}_(i=1)^N is denoted maxA or max_(i)a_i, and is equal to the last element of a sorted ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method (MINRES) and ...