Rosenbrook funcion with constraint
The goal is to find the parameter vector \mathbf{x} = [x_0, x_1]^T that minimizes the non - convex Rosenbrock objective function:
subject to the non-linear inequality constraint restricting the domain to the unit disk:
- **Initial Guess : \mathbf{ x}_0 = (0, 0)
Example 1C#
Optimal solution found Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found
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Rosenbrook funcion with constraint, Lower and Upperbound
Example 2C#
Optimal solution found Optimal solution found Optimal solution found Optimal solution found Optimal solution found ( 0.5000 0.2500 , 0.25, 1, -0.0763, , System.Collections.Generic.List`1[SepalSolver.IterationState])
Rosenbrock function with constraint
The goal is to find the parameter vector :math:\mathbf{x} = [x_0, x_1]^T that minimizes the non-convex Rosenbrock objective function:
\min_{\mathbf{x}} f(x_0, x_1) = 100(x_1 - x_0^2)^2 + (1 - x_0)^2
subject to the non-linear inequality constraint restricting the domain to the unit disk:
g(\mathbf{x}) = x_0^2 + x_1^2 - 1 \le 0
- Initial Guess: :math:\mathbf{x}_0 = (0, 0)
Example 3C#
Optimal solution found Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found Solving not completed Optimal solution found Optimal solution found Optimal solution found Optimal solution found
Showing the first 80 of 504 lines.
Rosenbrock function with constraint, Lower and Upperbound
Minimizes the Rosenbrock objective subject to a shifted circular inequality constraint combined with explicit lower (lb) and upper (ub) parameter boundaries:
g(\mathbf{x}) = (x_0 - 0.333)^2 + (x_1 - 0.333)^2 - 0.11111 \le 0
0.0 \le x_0 \le 0.5, \quad 0.2 \le x_1 \le 0.8
Example 4C#
Optimal solution found Optimal solution found Optimal solution found Optimal solution found Optimal solution found ( 0.5000 0.2500 , 0.25, 1, -0.0763, , System.Collections.Generic.List`1[SepalSolver.IterationState])
Unconstrained Derivative-Free Optimization with Fminsearch
When gradient information is unavailable or the objective is non-differentiable, Fminsearch uses the Nelder-Mead Simplex algorithm to locate the unconstrained global minimum at :math:\mathbf{x}^ = (1, 1) where :math:f(\mathbf{x}^) = 0.
- Initial Guess: :math:\mathbf{x}_0 = (-1.2, 1.0)
Example 5C#
( 1.0000 1.0000 , 4.4768823537358065E-13, 1, , , System.Collections.Generic.List`1[SepalSolver.IterationState])
Global Stochastic Optimization with Genetic Algorithm
For non-convex or multimodal objective functions where gradient-based solvers risk getting trapped in local minima, the Genetic Algorithm (GA) uses population-based operators to explore bounded search spaces without requiring an initial guess.
-2.0 \le x_0 \le 2.0, \quad -2.0 \le x_1 \le 2.0
Example 6C#
Stopping: no improvement for too long. ( 0.9387 0.8720 , False, 0.012145145679997998, 0x1 empty double row vector, 0x1 empty double row vector)