build-in optimization function for discrete date

I have a bivariate function with 100 known coordinate points. I want to find which one of these 100 points minimizes the function value. Is there any built-in MATLAB function for this? The optimization problem is straightforward, and I don't need a complex optimization algorithm, just one with sufficiently low time complexity.

[子青]

A = [0	258.623087554821
    0.328661075749555	259.722049421362
    0.657322151499110	260.821011287902
    0.985983227248666	261.919973154442
    1.31464430299822	263.018935020983
    1.64330537874778	264.117896887523
    1.97196645449733	265.216858754063
    2.30062753024689	266.315820620604
    2.62928860599644	267.414782487144
    2.95794968174600	268.513744353684
    3.28661075749555	269.612706220225
    3.61527183324511	270.711668086765
    3.94393290899466	271.810629953306
    4.27259398474422	272.909591819846
    4.60125506049377	274.008553686386
    4.92991613624333	275.107515552927
    5.25857721199288	276.206477419467
    5.58723828774244	277.305439286007
    5.91589936349199	278.404401152548
    6.24456043924155	279.503363019088
    6.57322151499110	280.602324885629
    6.90188259074066	281.701286752169
    7.23054366649022	282.800248618709
    7.55920474223977	283.899210485250
    7.88786581798933	284.998172351790
    8.21652689373888	286.097134218331
    8.54518796948844	287.196096084871
    8.87384904523799	288.295057951411
    9.20251012098755	289.394019817952
    9.53117119673710	290.492981684492
    9.85983227248666	291.591943551032
    10.1884933482362	292.690905417573
    10.5171544239858	293.789867284113
    10.8458154997353	294.888829150653
    11.1744765754849	295.987791017194
    11.5031376512344	297.086752883734
    11.8317987269840	298.185714750275
    12.1604598027335	299.284676616815
    12.4891208784831	300.383638483355
    12.8177819542327	301.482600349896
    13.1464430299822	302.581562216436
    13.4751041057318	303.680524082977
    13.8037651814813	304.779485949517
    14.1324262572309	305.878447816057
    14.4610873329804	306.977409682598
    14.7897484087300	308.076371549138
    15.1184094844795	309.175333415678
    15.4470705602291	310.274295282219
    15.7757316359787	311.373257148759
    16.1043927117282	312.472219015299
    16.4330537874778	313.571180881840];

r_starb = 16.6541049559731;
r_aft = 22.0243527832652;
r_fort = 37.0487055665303;
r_port = 12.8405787169798;

parameter_11_modified = @(x) power(2 * x(1) ./ ((1 + 1) * r_starb - (1 - 1) * r_port), 2) + ...
            power(2 * x(2) ./ ((1 + 1) * r_fort - (1 - 1) * r_aft), 2) - 1;

[B_modified, fval_modified] = fminsearch(@(i) parameter_11_modified(A(i,:)), randi(size(A, 1), 1, 1));

Index in position 1 is invalid. Array indices must be positive integers or logical values.

Error in solution>@(i)parameter_11_modified(A(i,:)) (line 61)
[B_modified, fval_modified] = fminsearch(@(i) parameter_11_modified(A(i,:)), randi(size(A, 1), 1, 1));

Error in fminsearch (line 336)
fxr = funfcn(x,varargin{:});

The first column of A represents the x-coordinate, and the second column represents the y-coordinate. Substitute these points into the equation of parameter_11_modified and find the values that minimize parameter_11_modified.

[子青]

Answer 1

[Steven Lord]

So you have the function values at 100 different points and you want to know for which of those points the function takes on its minimum value? Just call min on the array of function values with two outputs.

coords = rand(10, 2);
z = peaks(coords(:, 1), coords(:, 2));
% Just store the coordinates and value in a table for easy viewing
results = table(coords(:, 1), coords(:, 2), z, 'VariableNames', ["x coord", "y coord", "z"])

results = 10×3 table
    x coord    y coord         z     
    _______    ________    __________

     0.8518      0.6576        1.7875
     0.2147     0.27487    -0.0015709
     0.7616     0.88459        2.1235
    0.40425     0.86036         1.856
    0.98584     0.44561        2.4099
     0.6305    0.067516       0.89791
    0.64818      0.8218        1.7281
    0.48698     0.93397        2.4026
    0.81635     0.59551        1.6368
    0.28119     0.79769        1.4355

[minimumValue, minimumLocation] = min(z)

minimumValue = -0.0016

minimumLocation = 2

To identify the coordinates where the minimum value in z is located:

coordinatesWhereMinimumOccurs = coords(minimumLocation, :)

coordinatesWhereMinimumOccurs = 1×2

0.2147 0.2749