INTSOLVER: An interval based solver for Global Optimization: evrosenbrock(x) - File Exchange

Code covered by the BSD License

Highlights from
INTSOLVER: An interval based solver for Global Optimization

evallag (f, c, x, lambda) Evaluate the lagrangian system and it's first derivative in a pair
evbranin(x) Name: Branin
evbrown(x) Name: Brown's Almost Linear
evbullardbiegler(x) Name: Bullard&Biegler
evcg11(x)
evcg13(x)
evcg3(x)
evcombustion(x) Name: Equilibrium Combustion
eveasom(x) Name: Easom
evferraristronconi(x) Name: Ferraris&Tronconi
evfg11(x)
evfg13(x)
evfg3(x)
evgoldsteinprice(x) Name: Goldstein&Price
evgriewank(x) Name: Griewank
evhimmelblau(x) Name: Himmelblau
evhumpcamel(x) Name: Three Hump Camel
evkubicek(x) Name: Kubicek
evlevy(x) Name: Levy
evmichalewicz(x) Name: Michalewicz
evrastrigin(x) Name: Rastrigin
evrosenbrock(x) Name: Rosenbrock
evshubert(x) Name: Shubert
evsmith(x) Name: Smith
evtrigonometric(x) Name: Trigonometric
intdiv(a, b) Extended interval division. This implementation follows the technical
intksolve(f, x0, options) Apply the Krawczyk operator to test existence of zeros of a nonlinear
intmincon(f, x0, nonlcon, opt... Find the global minima of a function f inside a box x0 subject to
intminunc(f, x0, options) Find the global minima of a function f inside the box x0. The user must
intoptimget(options) Display parameters setted by an option vector. If no input arguments are
intoptimset() Create an optimization options vector. To change default settings on
intsolve(f, x0, options) Find all zeros of a nonlinear system of equations inside an
nonnullgs (X, x, b, M) Perform one step of the interval gauss seidel method to solve the problem
nullgs (X, x, b, M) Perform one step of the interval gauss seidel method to solve the problem
sibranin(type) Branin problem initial data.
sibrown(type) Brown Almost linear problem initial data.
sibullardbiegler(type) Bullard&Biegler problem initial data.
sicombustion(type) Combustion problem initial data.
sieasom(type) Rastrigin problem initial data.
siferraristronconi(type) Ferraris&Tronconi problem initial data.
sig11(type)
sig13(type)
sig3(type, n)
sigoldsteinprice(type) Goldstein&Price problem initial data.
sigriewank(type, n) Griewank's problem initial data.
sihimmelblau(type) Himmelblau problem initial data.
sihumpcamel(type) Three hump camel problem initial data.
sikubicek(type) Kubicek problem initial data.
silevy(type, n) Levy's problem initial data.
simichalewicz(type, n) Michalewicz's problem initial data.
sirastrigin(type, n) Rastrigin problem initial data.
sirosenbrock(type, n) Ronsenbrock's problem initial data.
sishubert(type) Shubert's problem initial data.
sismith(type) Smith problem initial data.
sitrigonometric(type, n) Trigonometric problem initial data.
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from INTSOLVER: An interval based solver for Global Optimization by Tiago Montanher
Interval based functions to solve small global optimization problems with guaranteed bounds.

evrosenbrock(x)

function y = evrosenbrock(x)

% Name: Rosenbrock
% Reference: 
% Testing Unconstrained Optimization. Moré J. J., Garbow B. S., Hillstrom
% K. E., 1981. ACM Trans. Math. Software, 136 - 140.
% Variables: n
% Initial Point/ Initial Interval: [(-1.2,...,-1.2)] /([-5,10],...,[-5,10])
% Reported Solution: (1,1,....,1)
% Minima: 0
% Matlab Code by A. Hedar (Nov. 23, 2005).


n = length(x);
sum = 0;

for j = 1:n-1;
    sum = sum + 100 * (x(j)^2-x(j+1))^2 + (x(j)-1)^2;
end

y = sum;

Highlights from INTSOLVER: An interval based solver for Global Optimization

Highlights from
INTSOLVER: An interval based solver for Global Optimization