Usage of scipy.optimize.fmin_slsqp

I'm trying to use the scipy.optimize package to find the maximum of my cost function. In this particular case: I have a list of prices which vary over the day. To make it easier, lets assume the day has 8 hours and the price in each hour are as follows: ``` price_list = np.array([1,2,6,8,8,5,2,1]) ``` In this simplified case I want to select the 4 highest prices from that price_list. And for various reasons I don't want to simply sort and select the best four prices, but use some optimization algorithm. I have several constraints, therefore I decided to use the least square algorithm from scipy, scipy.optimize.fmin_slsqp. I first create a schedule for the hours I select: ``` schedule_list = np.zeros( len(price_list), dtype=float) ``` Next I need to define my inversed profit_function. For all selected hours I want to sum up my profit. While I want to optimize my schedule, the price_list is fixed, therefore I need to put it to the *args: ``` def price_func( schedule_list, *price_list ): return -1.*np.sum( np.dot( schedule_list, price_list ) ) ``` Once I understand how things work in principle I will move some stuff around. So long, I simply avoid using more *args and define my constraint with a hard coded number of hours to run. And I want my selected hours to be exactly 4, therefore I use an equality constrain: ``` def eqcon(x, *price_list): return sum( schedule_list ) - 4 ``` Furthermore I want to restrict my schedule values to be either 0 or 1. I'm not sure how to implement this right now, therefore I simply use the bounds keywords. The unrestricted optimization with bounds works fine. I simply pass my schedule_list as first guess. ``` scipy.optimize.fmin_slsqp( price_func, schedule_list, args=price_list, bounds=[[0,1]]*len(schedule_list) ) ``` and the output is as good as it can be: ``` Optimization terminated successfully. (Exit mode 0) Current function value: -33.0 Iterations: 2 Function evaluations: 20 Gradient evaluations: 2 Out[8]: array([ 1., 1., 1., 1., 1., 1., 1., 1.]) ``` Without any further constraints, this is the optimal solution! Using the constrained optimization with the following command: ``` scipy.optimize.fmin_slsqp( price_func, schedule_list, args=price_list, bounds=[[0,1]]*len(schedule_list), eqcons=[eqcon, ] ) ``` gives me the error: ``` Singular matrix C in LSQ subproblem (Exit mode 6) Current function value: -0.0 Iterations: 1 Function evaluations: 10 Gradient evaluations: 1 Out[9]: array([ 0., 0., 0., 0., 0., 0., 0., 0.]) ``` From gnuplot I know that this is often related to non-sense questions or bad initial values. I tried almost optimal initial values, but that does not help. Does anybody has an idea or even solution for me? In a next step, I already have formulated inequality constrains. Do I understand it correctly that in the scipy minimize wrapper the inequalities are assumed to be larger than 0, while in fmin_slsqp it is vice versa. Solutions are constrained to negative constrain functions?