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Copy file name to clipboardExpand all lines: docs/src/example-double-integrator-energy.md
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```@example main
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# auxiliary in-place NLE function
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nle!(s, p0, λ) = s[:] = S(p0)
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nle!(s, p0, _) = s[:] = S(p0)
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# initial guess for the Newton solver
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p0_guess = [1, 1]
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## State constraint
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The following example illustrates both direct and indirect solution approaches for a constrained energy minimization problem. The workflow demonstrates a practical strategy: a direct method on a coarse grid first identifies the problem structure and provides an initial guess for the indirect method, which then computes a precise solution via shooting based on Pontryagin's Maximum Principle. The direct solution can also be refined using a finer discretization grid for higher accuracy.
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The following example illustrates both direct and indirect solution approaches for the energy minimization problem with a state constraint on the maximal velocity. The workflow demonstrates a practical strategy: a direct method on a coarse grid first identifies the problem structure and provides an initial guess for the indirect method, which then computes a precise solution via shooting based on Pontryagin's Maximum Principle.
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!!! note
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The direct solution can be refined using a finer discretization grid for higher accuracy.
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### Direct method: constrained case
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Copy file name to clipboardExpand all lines: docs/src/manual-solve.md
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# [Solve a problem](@id manual-solve)
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```@meta
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Draft = false
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```
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This manual explains how to use the [`solve`](@ref) function to solve optimal control problems with OptimalControl.jl. The `solve` function provides a **descriptive mode** where you specify strategies using symbolic tokens, with automatic option routing and validation.
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