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This question is commonly asked for Data Scientist candidates at Imc during technical interviews.

Solve a constrained problem using KKT conditions

Last updated: Mar 29, 2026

Quick Overview

This question evaluates understanding of constrained optimization using Karush–Kuhn–Tucker (KKT) conditions, including Lagrangian formulation, stationarity, complementary slackness, dual feasibility, and identification of active constraints.

Imc

Jan 14, 2026, 12:00 AM

Data Scientist

Onsite

Machine Learning

Use Karush–Kuhn–Tucker (KKT) conditions to solve the following constrained optimization problem:

Minimize

$\min_{x,y}\; f(x,y)=x^2+y^2$

subject to

$x+y \ge 1$
$x \ge 0$
$y \ge 0$

Tasks:

Write the Lagrangian and KKT conditions (stationarity, primal feasibility, dual feasibility, complementary slackness).
Identify which constraints are active at the optimum.
Solve for $(x^*,y^*)$ and the optimal value.

Solution

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