New answers tagged karush-kuhn-tucker
0
votes
Mathematical explanation of the intuition behind the Lagrange multiplier
From the f.o.c. for utility maximization under a budget constraint, we have
$$\frac{\partial U}{\partial x} = \lambda p_x,\;\;\;\frac{\partial U}{\partial y} = \lambda p_y$$
that holds at the optimal ...
2
votes
Accepted
Stationarity in KKT condition
In general, you don't know before you find them, which, if any, of the minimizers $\ \hat{x}\ $ will satisfy the condition $\ G(\hat{x})<0\ $, and if $\ \hat{x}\ $ is a local minimizer for which $\ ...
Top 50 recent answers are included
Related Tags
karush-kuhn-tucker × 444optimization × 324
convex-optimization × 158
nonlinear-optimization × 133
lagrange-multiplier × 108
convex-analysis × 32
quadratic-programming × 27
linear-programming × 25
constraints × 25
solution-verification × 17
duality-theorems × 16
non-convex-optimization × 15
multivariable-calculus × 13
calculus × 10
linear-algebra × 9
real-analysis × 8
numerical-optimization × 8
operations-research × 8
qcqp × 8
economics × 7
maxima-minima × 6
calculus-of-variations × 6
machine-learning × 5
projection × 5
constraint-programming × 5