Algorithm for finding the location of the expected saddle point of stationary points of a function of two variables in the coordinate descent-ascent method

[img]https://cdn.geogebra.org/resource/tappbhca/9HmYQ3S1CbDWBu2r/material-tappbhca.png[/img]
[size=100][size=150][b] Algorithm for finding the location of the expected [color=#6aa84f]saddle point[/color] of stationary points of a function of two variables in the coordinate descent-ascent method[br][/b][size=85] I used[br]- contour map or heat map to approximate the location of stationary points for a function of two variables,[br]- GeoGebra[b] [color=#ff0000]Maximize[/color]/[color=#0000ff]Minimize[/color] [/b]commands and the coordinate [b][url=https://en.wikipedia.org/wiki/Coordinate_descent]ascent/descent[/url][/b] method. The iterative method for finding stationary points for cases of saddle points was developed by me - I did not find corresponding numerical methods in the literature.[br] At each iteration step we have a new point [b]E[sub]i+1[/sub][/b], and then the interval of change around the new point decreases [b][b][color=#0000ff]↘[/color][/b][/b]: [x([b]E[sub]i[/sub][/b])-p, x([b]E[sub]i[/sub][/b])+p] and correspondingly [y([b]E[sub]i[/sub][/b])-p, y([b]E[sub]i[/sub][/b])+p]. p is the radius of the circle described around new point [b]E[/b]. po is the initial radius, then it decreases according to the law p:=p*q. My q=0.75.[br] [/size][/size][/size][size=85][b] A [color=#38761d]saddle point[/color], which seems to divide a function into two halves of [color=#ff0000]growth[/color] [b][color=#ff0000]↗[/color][/b] and [color=#0000ff]decrease[/color] [b][color=#0000ff]↘[/color] [/b]of the function.[br] ➤On the contour map, we draw a circle with the center [color=#6aa84f]E[/color] at the point of the selected initial approximation of the [color=#6aa84f]saddle point [/color]search and with a radius p, which is initially an iterative process p0 and then gradually decreases [b][color=#0000ff]↘[/color][/b] according to a preselected law.[br] ➤On this circle we will find characteristic points [color=#ff7700]B01 [/color][color=#333333]and [/color][color=#1e84cc]B02[/color]: the [color=#ff0000]maximum[/color] value [i]a1[/i] of the function (using the [color=#ff0000]Maximize[/color] command) and the [color=#0000ff]minimum[/color] value (again a1) of the function (using the [color=#0000ff]Minimize[/color] command). Here we [i]will assume[/i] that on the circle, symmetrically with respect to the center of the circle, these points have "doubles" - points [color=#ff7700]B1[/color] and [color=#1e84cc]B2[/color] also of the [color=#ff0000]maximum[/color] and [color=#0000ff]minimum[/color] values of the function. In the direction of the [color=#ff0000]largest[/color] values of the function it [color=#ff0000]increases[/color][color=#ff0000] [b]↗[/b][/color], and in the direction of the [color=#1e84cc]smallest[/color] values it [color=#1e84cc]decreases [b][b][color=#0000ff]↘[/color][/b][/b][/color].[br] ➤Iteration Cycle: : Let's connect these point pairs of "[color=#ff0000]hot[/color]" and "[color=#0000ff]cold[/color]" points with segments [color=#ff7700]f1[/color] and [color=#1e84cc]f2[/color]. First, along the first segment [color=#ff7700]f1[/color] we find the coordinates of the point with the [color=#0000ff]minimum[/color] value a1 of the function - it is a new position ([color=#ff0000]E[/color]) of the [color=#6aa84f]saddle point [/color][color=#ff00ff]U1[/color]. Again, on the newly drawn circle, we find the coordinates of the point B02 of the smallest values a1 of the function and, accordingly, its "double" B2. We will connect the "[color=#9900ff]cold[/color]" points with the segment [color=#1e84cc]f2[/color] and find the coordinates of the point [color=#1e84cc]U2[/color] where the function takes the [color=#ff0000]maximum[/color] value. This will be the new position E of the [color=#6aa84f]saddle point[/color].[br] We repeat this cycle many times in the "hope" that the centers of these segments should coincide. [i]Convergence[/i] is always in question![/b][/size]
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[/img][/td][td][table][tr][td][size=85][b][u]button15[/u][br]SetValue[a1,[color=#ff0000]Maximize[/color][ f(x(Point(d, a0) ),y(Point(d, a0) )) , a0 ] ][br]SetValue[[color=#ff7700]B01[/color],Point(d, a1) ][br] SetValue[[color=#ff7700]B1[/color],Rotate([color=#ff7700]B01[/color] , 180°, [color=#ff0000]E[/color]) ][br] [br][u]button16[/u][br] SetValue[a1,[color=#0000ff]Minimize[/color][ f(x(Point([color=#ff7700]f1[/color], a0) ),y(Point([color=#ff7700]f1[/color], a0) )) , a0 ] ][br] SetValue[[color=#ff00ff]U1[/color],Point([color=#ff7700]f1[/color], a1) ][br][br][u]button17[/u][br]SetValue[a1,[color=#0000ff]Minimize[/color][ f(x(Point(d, a0) ),y(Point(d, a0) )) , a0 ] ][br] SetValue[[color=#1e84cc]B02[/color],Point(d, a1) ][br] SetValue[[color=#1e84cc]B2[/color],Rotate(B02 , 180°,[color=#ff0000]E[/color]) ][br][br][u]button18[/u][br] SetValue[a1,[color=#ff0000]Maximize[/color][ f(x(Point([color=#1e84cc]f2[/color], a0) ),y(Point([color=#1e84cc]f2[/color], a0) )) , a0 ] ][br] SetValue[[color=#1e84cc]U2[/color],Point([color=#1e84cc]f2[/color], a1) ][br][/b][/size][/td][/tr][tr][td][br][/td][td][/td][/tr][/table][/td][/tr][/table][size=85][b] ●For the case with functions given in [color=#9900ff]explicit[/color] form, [url=https://www.geogebra.org/m/z4esav5y]e.g[/url].:[/b] [b][u]button19[/u][/b][br]Execute[{"RunClickScript([b] button15[/b]) ", "RunClickScript( [b]button16[/b] ) ", "SetValue[[b][color=#ff7700]E[/color][/b], [b][color=#ff00ff]U1[/color][/b]]" ,"RunClickScript( [b]button17[/b]) ", "RunClickScript( [b]button18[/b]) ", "SetValue[[b][color=#ff7700]E[/color][/b], [color=#1e84cc][b]U2[/b][/color]]" }]; dU=CopyFreeObject( Distance[[color=#1e84cc][b]U2[/b][/color],[b][color=#ff00ff]U1[/color][/b]]/p0 ) [b]⮕[/b] d[sub]i[/sub]:=dU[br][br][b] ●For the case with functions given in [color=#9900ff]numerical[/color] form, [url=https://www.geogebra.org/m/djykrvyv]e.g[/url]. :[/b] [b][u]button19[/u][/b][br]Execute[{"RunClickScript( [b]button15[/b] ) ", "RunClickScript( [b]button16[/b] ) ", "RunClickScript( [b]button17[/b] ) ", "RunClickScript( [b]button18[/b] ) ", "SetValue[[b][color=#ff7700]E[/color][/b], [b][color=#ff00ff]U1[/color][/b]]" }][br]Execute[{"RunClickScript( [b]button15[/b]) ", "RunClickScript( [b]button16[/b] ) ", "RunClickScript( [b]button17[/b]) ", "RunClickScript( [b]button18[/b]) ", "SetValue[[b][color=#ff7700]E[/color][/b], [b][color=#1e84cc]U2[/color][/b]]" }]; dU=CopyFreeObject( Distance[[b][color=#1e84cc]U2[/color][/b],[b][color=#ff00ff]U1[/color][/b]]/p0 )[b]⮕[/b] d[sub]i[/sub]:=dU[/size]
[size=85] The [i]iterative cycle[/i] under consideration turned out to be productive. Evaluation As calculations have shown, the algorithm using only the [b][color=#ff00ff]U1[/color][/b] or only the [color=#1e84cc]U2[/color] sequence has poor convergence.[br] To calculate [b][color=#6aa84f]saddle points[/color][/b], [b]di[/b] - the distance between two characteristic points [b][color=#ff00ff]U1[/color][/b] and [b][color=#1e84cc]U2[/color][/b] for each iteration - was chosen as a [i][b]estimated parameter[/b][/i]. After [b][color=#0000ff]no[/color][/b]+2 iteration steps, the smallest one is selected from all these estimated parameters. These distances are sufficiently different for different iterations that the calculations can be done in the GeoGebra algebra without using CAS.[/size]
An example of such a calculation is given here.
[size=85] [b][color=#980000]ClosestPoint[/color][/b] is a [b][color=#6aa84f]saddle point[/color][/b] found earlier using [b]CAS[/b]. [b]f[sub]x[/sub][/b] and [b]f[sub]y[/sub][/b] are partial derivatives at this [b][color=#980000]point [/color][/b]and at the [color=#ff00ff][b]point[/b][/color] found by the proposed method. Here it is iteration [b][color=#6aa84f]30[/color][/b] in the list above. For stationary points, these derivatives are zero. As can be seen, the iterative calculations are performed with a high degree of accuracy. [color=#ff7700][b](f[/b][sub]x[/sub][b],f[/b][sub]y)[/sub][/color][b][color=#ff7700]/f [/color]-[/b][color=#333333]We consider it as a "relative" error.[/color][/size]
[size=85]Applets explaining algorithms for calculating stationary points:[br][url=https://www.geogebra.org/m/ef6s3hyj]Algorithm[/url] for finding the location of local maxima or minima [br][url=https://www.geogebra.org/m/hcgdjdyf]Algorithm[/url] for finding the location of the saddle point [br][br]*Examples of using the described algorithms can be found in the applets: [url=https://www.geogebra.org/m/eyqphb7g]1[/url], [url=https://www.geogebra.org/m/qktn5chb]2[/url], [url=https://www.geogebra.org/m/hmq7asxa]3[/url], [url=https://www.geogebra.org/m/z4esav5y]4[/url], [url=https://www.geogebra.org/m/djykrvyv]5[/url].[/size]

Information: Algorithm for finding the location of the expected saddle point of stationary points of a function of two variables in the coordinate descent-ascent method