Quickstart

Solve your first optimization problem in 5 minutes

Published

February 8, 2026

1 Your First Optimization Problem

Let’s solve a simple constrained optimization problem:

\[ \min_{x,y} \quad x^2 + y^2 \quad \text{subject to} \quad x + y \geq 1 \]

from optyx import Variable, Problem

# 1. Create decision variables
x = Variable("x", lb=0)  # x ≥ 0
y = Variable("y", lb=0)  # y ≥ 0

# 2. Build and solve the problem
solution = (
    Problem()
    .minimize(x**2 + y**2)
    .subject_to(x + y >= 1)
    .solve()
)

# 3. Access the results
print(f"x* = {solution['x']:.4f}")
print(f"y* = {solution['y']:.4f}")
print(f"Objective = {solution.objective_value:.4f}")
print(f"Status = {solution.status}")

x* = 0.5000
y* = 0.5000
Objective = 0.5000
Status = SolverStatus.OPTIMAL

Inspect Your Problem

Use print(problem.summary()) to get a quick overview of your problem’s structure before solving.

The optimal solution is \(x^* = y^* = 0.5\), which satisfies the constraint \(x + y = 1\) at equality.

2 Step-by-Step Breakdown

2.1 1. Create Variables

Variables are your decision variables—the values the solver will optimize:

from optyx import Variable

# Basic variable (unbounded)
x = Variable("x")

# Variable with lower bound
y = Variable("y", lb=0)

# Variable with both bounds
z = Variable("z", lb=-10, ub=10)

Scaling Up

For problems with many variables, use VectorVariable instead of creating individual Variable objects. See Vector Variables for details.

2.2 2. Build Expressions

Use natural Python operators to build objective functions:

from optyx import sin, exp

# Arithmetic works naturally
objective = x**2 + 2*y**2 + x*y

# Transcendental functions are supported
nonlinear_obj = sin(x) + exp(-y)

# Evaluate at a point
value = objective.evaluate({"x": 1.0, "y": 2.0})
print(f"f(1, 2) = {value}")

f(1, 2) = 11.0

2.3 3. Define Constraints

Express constraints with comparison operators:

from optyx import Variable, Problem

a = Variable("a", lb=0)
b = Variable("b", lb=0)

prob = (
    Problem()
    .minimize(a**2 + b**2)
    .subject_to(a + b >= 1)          # Inequality: a + b ≥ 1
    .subject_to(a <= 5)              # Upper bound as constraint
    .subject_to((a - b).eq(0))  # Equality: a = b
)

Note

For equality constraints, use .eq() instead of == because Python’s == is used for object comparison.

2.4 4. Solve and Inspect

solution = prob.solve()

print(f"Status: {solution.status}")
print(f"Objective: {solution.objective_value:.4f}")
print(f"Solve time: {solution.solve_time:.4f}s")
print(f"Iterations: {solution.iterations}")

Status: SolverStatus.OPTIMAL
Objective: 0.5000
Solve time: 0.0008s
Iterations: 3

3 Maximization

Optyx supports maximization too:

from optyx import Variable, Problem

x = Variable("x", lb=0, ub=10)
y = Variable("y", lb=0, ub=10)

solution = (
    Problem()
    .maximize(x + 2*y)
    .subject_to(x + y <= 8)
    .subject_to(x <= 5)
    .solve()
)

print(f"x* = {solution['x']:.2f}, y* = {solution['y']:.2f}")
print(f"Maximum = {solution.objective_value:.2f}")

x* = 0.00, y* = 8.00
Maximum = 16.00

4 Next Steps

Core Concepts — Deeper understanding of expressions, constraints, and problems
Basic Optimization Tutorial — More detailed walkthrough
API Reference — Full API documentation