This is soooooo awesome. Thank you! I have been learning python for months....this is the first time that I have solved an optimization problem

I've been looking a lot of your videos and they have help me a lot, thank you very much.

You just saved me like a century trying to figure out how to unroll these summed values. Thanks!

Thanks for the short and clear explanation. Thanks for clearing the fear I have of equations and coding. Thanks for being so kind to reply to every query in the comments section . Thanks for designing the course and uploading the videos Thanks for helping many students like me. You increased my confidence and changed my perception..that I can do more. I wish you get what you deserve. You will be remembered :) Thank you, Sir!!!!

Wow!Best Intro Ever..looking forward to more stuff like this

Thank you for your help. We have an assignment next week and the last question is exactly the same ! :)

This gave me hope for my thesis. Thank you sir :D

I have no words to thank you, love from India

Many thanks sir for such a great and clear instruction on solving LP in python.

This video saved me a big headache, thank you!

It’s very clear, thanks!

absolutely amazing tutorial!

I wish I would have found you 1-hour earlier. Thank you! So clear and helpful. Ahhhh

Very helpful and educational sir. Thank you so much for your videos

Thank you veryy much for this. Awesome one

Thank you for clear and simple explanation

Thanks so much. So much clearer now!

quick and to the point. Thank you!

Awesome Video! Very clear and helpful!!! Thanks!

Thank you! This helped a lot.

At 0:39 I think you must write a "sumation" of terms squared sum x_i^2=40 not a product.

Short and concise, thanks

Thank you for the explanation. There is a slip of tongue at 0:30 where you said the product. It's the summation of x_i.squared. Thanks

Great tutorial!

Thank you, very helpful!

It's great 👍 Thanks for simple learning.

Awesome! thank you.

Great video. Very helpful for the implementation of the code. I had a quick question though. How would one extract the design point history from each iteration? I ask because I have to do a tracking of the history as it converges to the minimizer. Thanks a ton!

I'm new to the optimization field and found the video very useful. Is the example mentioned in the video QCQP (quadratically constraint quadratic programming?)

Thx a lot for this tutorial! There is something puzzling me with the result though. The solution x you're getting is not a minimizer since the objective funtion evaluated at this point is 17, which is greater than the initial guess' objective 16. Why is that ?

Nice job!

Great video..

Thank you sir for this demo. Could you please let me know if there is any implementation of finding pareto optimal points for multi object optimization problems (eg two variable) using Scipy.

thank you sir, god bless you

Thanks a lot.

Thanks for this very approachable intro to using Python to do optimization. What book(s) can you recommend specifically for Python and optimization?

Note for someone, who has less or equal inequality constraint. Docs: Equality constraint means that the constraint function result is to be zero whereas inequality means that it is to be non-negative. You need to multiply constraint by -1 to reverse the sign.

Thanks for the video! Does it matter if the constraint is < or > for the method? Should it be in the standard form like for LP?

Great! Thanks.

Is there any way to keep some of the variables constant? Like those variables are in the objective function, but we don't want to solve for those values? Or is the only way is to keep them with same values for lb and ub in bounds

Awesome, thanks

Hello APMonitor, thank you for making such wonderfull videos. I have a little problem, i tried adapting the optimization with Nested List but scipy doesnt seem to understand the structure so changed my model to Numpy array which it understands but gives me the error : "indexing a scalar" error. If u can show me how to implement the optimization using arrays that would be really helpfull.

Great video; it helped me a lot. Just wondering tho, if u wanted your bounds to be, say, STRICTLY greater than 1 and STRICTLY less than 5 (i.e. 1

Hi thanks for the video. For example like this problem which algorithm (genetic, simulated annealing, particle swarm) can we apply and how?

Thank you, Prof. Hedengren. Noting that this video was posted five years ago, do you think in 2022 there is still a case for using SciPy for optimization tasks instead of using GEKKO? In particular, GEKKO’s MINLP does not have an equivalent within SciPy. Is there any optimization task where SciPy would still be required instead of using GEKKO?

Fantastic video. What is the best way to add bounds for multiple variables; say more than 24 (optimizing across time, 12 months)? I definitely don't want to list them all......perhaps loop through the variable matrix....but hopefully a more efficient way? Thanks!

Hi, what i noticed, if you put the x0 you`ll get 16 and if you use the `minimize` function, it will give you an array that result around 17. But isn`t that mean our goal with `minimize` function hasn`t been fulfilled yet?

Great video. May I know if the minimize function is basically finding the root of x1x4(x1+x2+x3)+x3=0 equation? This would help a lot. Sorry for dumb question. Thanks!

Hello Jhon. I am wondering if you have any material related to python and OR. I am learning myself OR for one side and python for another side. I am wondering if there is any book in which I can combine them. Do you have any material that I can access to or course? Looking forward to hearing from you. Paul.

Hello ApMonitor, great video, a question, how much is the capacity of Scipy? has it a restriction about number of variables or constraints? to solve, for example, the Vehicle routing problem, has it capacity?

Método dos mínimos quadrados esse!

Does the initial set of x minimize the function? the result of your code shows the f(x)=17.01..., which is larger than 16 why is that?

what happens if there are multiple solutions? I mean there is more than 1 set of x1, x2, x3, x4 for solution...are they all stock into the final array (which will become multi dimentional)? thanks

Why do you use x1, x2, x3, x4 in returning the objective function but then switch to using x[0], x[1], x[2], x[3] in the constraint functions? I'm not trying to be pedantic, but it would help me if it was consistent either one way or the other, unless there's a reason that they're like that? e.g. could the constraint1(x) function be written as return x1 * x2 * x3 * x4 - 25 instead? (purely to be consistent) and/or could you write constraint1 in the same way you did for constraint2: using a for loop? e.g. def constraint1(x): product = 1 for i in range(4): product = product * x[i] return product - 25 or instead write constraint2(x) as you did with the objective function return (and as I did with constraint1(x) above): using x1, x2, x3, x4 instead of x[i]. This way it is consistent and may be easier for people who aren't good coders or mathematicians to follow along perhaps.. (I apologise if these are bad questions/suggestions - I am not a programmer, just trying to learn, and in this case understand why you wrote things out in 3 different ways instead of 1..) Thank you kindly for any help in understanding (and of course for the video itself - cheers)!

In the end fun value turned out to be greater than the initial guess? Is it optimized? What am I missing?

can you get solution of "maximum ellipse on certain polygon?" using optimize library? for example A(x-x0)^2 + B(y-y0)^2 = 1 st. set of linear constraints which describe polygon on X-Y space. And I need to get best x0,y0 which minimize A*B

How can we compute the errors associated to the fitted parameters?

Thank you very much for your tutorial. Does Scipy minimize function require data?

hi, why is the min objective with the initial guess numbers lower than the min objective at the end? shouldn't the solver return the lowest value of the function?

Sir is there any advantages or disadvantages in using existing methodologies such as artificial neural networks, fuzzy logic and genetic algorithms to optimization of a linear objective function, subject to linear equality and linear inequality constraints over the Scipy method? I think Scipy method will provide accurate results in short time compared to other methods, since complexity of the linear problem is less.

Thanks

What's the difference between the "ineq' and 'eq' designations on the constraints?

Easy and lucid style

But how how come the minimization gave an objective function higher than before. You see initially your guess gave this to be equal to 16. After minimization, it was 17.014....... Shouldnt minimization minimize the objective function and return the points that give a value, even smaller than that of the guess?

Hello @APMonitor, thanks for this video. I have one doubt. I am trying to use SciPy.Optimize with Pandas dataframe. I want to minimize my target columns based on other columns. Can you please tell how to do that?

I have a question. If we change the guess, for instance 1 for all values, the script gives also 1 values as results for the variables and that´s totally wrong. So what could be the problem here?

Thanks for the video, but how do l do if my objective is maximizing

is the minimization function (function) based on the descent gradient?

Hi, do you have any idea why i'm getting this: "C:\Python34\lib\site-packages\scipy\optimize\slsqp.py:341: RuntimeWarning: invalid value encountered in greater bnderr = where(bnds[:, 0] > bnds[:, 1])[0]"? I'm getting the result, but i'm afraid this error is messing up the results. Edit: seems it has something to do with the infinte bound. I read somewhere that to specify a infinite bound you had to input None(ex: b = (0,None))

Nice!!! Any example for Multi-Objective Linear Programming? ???

This is for just two constraints. What if we have N constraints and, due to the way the problem is posed, we cannot use matrices. How do we use a generic constraint function N times in this case?

Is there a way to use scipy.optimize.minimize with only integer values?

I have a question. I attempted to maximize the function but couldn't get it to work right. What do I need to change? Thank you for your help! This is what I did: def objective(x, sign=1.0): x1 = x[0] x2 = x[1] x3 = x[2] x4 = x[3] return sign*(x1*x4*(x1+x2+x3)+x3) def constraint1(x): return x[0]*x[1]*x[2]*x[3]-25.0 def constraint2(x): sum_sq = 40 for i in range(4): sum_sq = sum_sq - x[i]**2 return sum_sq sol2 = minimize(objective,x0,args=(-1.0,),method='SLSQP',\ bounds=bnds,constraints=cons) But it gave me this (it went beyond constraint1) print(sol2) fun: -134.733824524366 jac: array([-45.75387001, -16.64193916, -17.64193916, -36.49635124]) message: 'Optimization terminated successfully.' nfev: 68 nit: 11 njev: 11 status: 0 success: True x: array([4.56763313, 1.66137361, 1.76120447, 3.64344948]) print(objective(sol2.x,1)) print(constraint1(sol2.x)) print(constraint2(sol2.x)) 134.733824524366 23.69462805071327 -1.0361844715589541e-10

hello thank you for your video I am wondering how it is possible to solve this problem without initial guess. I tried to remove initial guess but, looks like, initial guess should be provided as an argument to minimize(). Any advise will be highly appreciated

I got lost around 2:00 and now I'm mot sure where or even who I am anymore.

Could you point out how to possibly write a set of thousands of constraints using matrices and get them ready for scipy.optimize.minimize? In real world, the number of variables can be easily thousands. I'm dealing with a portfolio construction problem and I'm faced with thousands of variables. Thank you!

Why the optimized value 17.014 is even larger than the initial guess, 16?

at 4:15, you said to move everything to the right side for the second constraint, but what if I move everything to the left side, then write the program according to that. I did that, and the answer is different from yours. whys that...? x = [1,5,5,1] constraint2(x) returns -12 that is what your program is doing but with mine, it return 12

Am I getting this right? Objective function was 16 with the initial values (1,5,5,1) was 16 and after the final solution it was 17.0141. Am I interpreting something incorrectly?

Hi, shouldn't equation for sum_sq be sum_sq = 40 - x[i]**2 instead of what you wrote. I got different results when I compared them.

How does Scripy compare with AMPL, GAMS , AIIMS ?

Good !!

Sir, can you please demonstrate trust region algorithm implementation?

Question: x1*x2*x3*x4 >= 25 why we take 25 to the left not all the x to the right? x1^2+x2^2+x3^2+x4^2 = 40 why we take all the x to the right not 40 to the left?

what if it was strictly larger than 25, what would you type then

I'm sorry, but it only undertakes how this method is implemented in Python rather than digging into the method itself (i.e. what does *exactly* a SLSQP method do?)

can we use Scipy.Optimize.Minimize for integer LP?

How would you do this for integers only?

Sir, I wrote some comments here in response to the recent materials you recommended me to read. but, seem omitted? Am I right?

Thanks! But what about maximum? Can you explain?

Can you explain use of this as well so it will be useful for beginners like me to understand

How can we implement "strict less than" constraint?

if x[i] is a large array x[100] for example, do we need to write down all the numbers in the array for the initial guess x0???

Sir i have alot of questions about optimize with python, and i have some model that i shuld to finish. So can i get your contact sir?

which are Lagrange multipliers at the solution?

can any one help me to carry out multi objective optimisation using PYTHON?

Sir, could you please make a video lecture on L2 norm minimization under some constraints for any scenario using python from scratch? Thanks again for the great lecture!

File "main.py", line 22 sol=minimize(objective,x0,method='SLSQP',\ bounds=bnds,constraints=cons) ^ SyntaxError: unexpected character after line continuation character , now am getting this in last line, help me to get out of this

Hello! I studied your program a lot in Python and a question arose. If by chance, sum_sq = 400.0 and not 40, constraint2 is not satisfied because constraint2 ~ 300.024 and should be 0. Why does the program continue to provide a solution for x1 up to x4 if constraint 2 is not met? Please, I would like your help to interpret this. Thanks, Luciana from Brazil.

APMonitor.com How did you choose your starting shot for x0?