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Copy file name to clipboardExpand all lines: doc/2-PROXQP_API/2-ProxQP_api.md
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@@ -67,11 +67,11 @@ It is important to note that this stopping criterion on primal and dual residual
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$$\begin{equation}\label{eq:approx_dg_sol}
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\begin{aligned}
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r_g := | x^T H x + g^T x + b^T y + u^T [z]_+ + l^T [z]_- | \leq \epsilon_{\text{abs}} + \epsilon_{\text{rel}} \max(\|x^T H x\|, \|g^T x\|, \|b^T y\|, \|u^T [z]_+\|, \|l^T [z]_-\|), \\
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r_g := | x^T H x + g^T x + b^T y + u^T [z]_+ + l^T [z]_- | \leq \epsilon^{\text{gap}}_{\text{abs}} + \epsilon^{\text{gap}}_{\text{rel}} \max(\|x^T H x\|, \|g^T x\|, \|b^T y\|, \|u^T [z]_+\|, \|l^T [z]_-\|), \\
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\end{aligned}
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\end{equation}$$
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where $[z]_+$ and $[z]_-$ stand for the projection of z onto the positive and negative orthant. ProxQP provides the ``check_duality_gap`` option to include this duality gap in the stopping criterion. Note that it is disabled by default, as other solvers don't check in general this criterion. Enable this option if you want a stronger guarantee that your solution is optimal. ProxQP will then check the same termination condition as SCS (for more details see, e.g., SCS's [optimality conditions checks](https://www.cvxgrp.org/scs/algorithm/index.html#optimality-conditions) as well as [section 7.2](https://doi.org/10.1137/20M1366307) in the corresponding paper). Note finally that meeting all these criteria can be difficult for ill-conditioned problems.
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where $[z]_+$ and $[z]_-$ stand for the projection of z onto the positive and negative orthant. ProxQP provides the ``check_duality_gap`` option to include this duality gap in the stopping criterion. Note that it is disabled by default, as other solvers don't check in general this criterion. Enable this option if you want a stronger guarantee that your solution is optimal. ProxQP will then check the same termination condition as SCS (for more details see, e.g., SCS's [optimality conditions checks](https://www.cvxgrp.org/scs/algorithm/index.html#optimality-conditions) as well as [section 7.2](https://doi.org/10.1137/20M1366307) in the corresponding paper). The absolute and relative thresholds $\epsilon^{\text{gap}}_{\text{abs}}, \epsilon^{\text{gap}}_{\text{rel}}$ for the duality gap can differ from those $\epsilon_{\text{abs}}, \epsilon_{\text{rel}}$ for residuals because, contrary to residuals which result from an infinite norm, the duality gap scales with the square root of the problem dimension (thus it is numerically harder to achieve a given duality gap for larger problems). A recommended choice is $\epsilon^{\text{gap}}_{\text{abs}} = \epsilon_{\text{abs}} \sqrt{\max(n, n_{\text{eq}}, n_{\text{ineq}})}$. Note finally that meeting all residual and duality-gap criteria can be difficult for ill-conditioned problems.
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\section OverviewAPIstructure ProxQP unified API for dense and sparse backends
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| eps_abs | 1.E-5 | Asbolute stopping criterion of the solver.
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| eps_rel | 0 | Relative stopping criterion of the solver.
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| check_duality_gap | False | If set to true, include the duality gap in absolute and relative stopping criteria.
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| eps_duality_gap_abs | 1.E-4 | Asbolute duality-gap stopping criterion of the solver.
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| eps_duality_gap_rel | 0 | Relative duality-gap stopping criterion of the solver.
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| VERBOSE | False | If set to true, the solver prints information at each loop.
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| default_rho | 1.E-6 | Default rho parameter of result class (i.e., for each initial guess, except WARM_START_WITH_PREVIOUS_RESULT, after a new solve or update, the solver initializes rho to this value).
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| default_mu_eq | 1.E-3 | Default mu_eq parameter of result class (i.e., for each initial guess, except WARM_START_WITH_PREVIOUS_RESULT, after a new solve or update, the solver initializes mu_eq to this value).
Copy file name to clipboardExpand all lines: doc/3-ProxQP_solve.md
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@@ -67,11 +67,11 @@ It is important to note that this stopping criterion on primal and dual residual
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$$\begin{equation}\label{eq:approx_dg_sol}
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\begin{aligned}
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r_g := | x^T H x + g^T x + b^T y + u^T [z]_+ + l^T [z]_- | \leq \epsilon_{\text{abs}} + \epsilon_{\text{rel}} \max(\|x^T H x\|, \|g^T x\|, \|b^T y\|, \|u^T [z]_+\|, \|l^T [z]_-\|), \\
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r_g := | x^T H x + g^T x + b^T y + u^T [z]_+ + l^T [z]_- | \leq \epsilon^{\text{gap}}_{\text{abs}} + \epsilon^{\text{gap}}_{\text{rel}} \max(\|x^T H x\|, \|g^T x\|, \|b^T y\|, \|u^T [z]_+\|, \|l^T [z]_-\|), \\
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\end{aligned}
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\end{equation}$$
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where $[z]_+$ and $[z]_-$ stand for the projection of z onto the positive and negative orthant. ProxQP provides the ``check_duality_gap`` option to include this duality gap in the stopping criterion. Note that it is disabled by default, as other solvers don't check in general this criterion. Enable this option if you want a stronger guarantee that your solution is optimal. ProxQP will then check the same termination condition as SCS (for more details see, e.g., SCS's [optimality conditions checks](https://www.cvxgrp.org/scs/algorithm/index.html#optimality-conditions) as well as [section 7.2](https://doi.org/10.1137/20M1366307) in the corresponding paper). Note finally that meeting all these criteria can be difficult for ill-conditioned problems.
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where $[z]_+$ and $[z]_-$ stand for the projection of z onto the positive and negative orthant. ProxQP provides the ``check_duality_gap`` option to include this duality gap in the stopping criterion. Note that it is disabled by default, as other solvers don't check in general this criterion. Enable this option if you want a stronger guarantee that your solution is optimal. ProxQP will then check the same termination condition as SCS (for more details see, e.g., SCS's [optimality conditions checks](https://www.cvxgrp.org/scs/algorithm/index.html#optimality-conditions) as well as [section 7.2](https://doi.org/10.1137/20M1366307) in the corresponding paper). The absolute and relative thresholds $\epsilon^{\text{gap}}_{\text{abs}}, \epsilon^{\text{gap}}_{\text{rel}}$ for the duality gap can differ from those $\epsilon_{\text{abs}}, \epsilon_{\text{rel}}$ for residuals because, contrary to residuals which result from an infinite norm, the duality gap scales with the square root of the problem dimension (thus it is numerically harder to achieve a given duality gap for larger problems). A recommended choice is $\epsilon^{\text{gap}}_{\text{abs}} = \epsilon_{\text{abs}} \sqrt{\max(n, n_{\text{eq}}, n_{\text{ineq}})}$. Note finally that meeting all residual and duality-gap criteria can be difficult for ill-conditioned problems.
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\section OverviewAsingleSolveFunction A single solve function for dense and sparse backends
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| eps_abs | 1.E-5 | Asbolute stopping criterion of the solver.
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| eps_rel | 0 | Relative stopping criterion of the solver.
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| check_duality_gap | False | If set to true, include the duality gap in absolute and relative stopping criteria.
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| eps_duality_gap_abs | 1.E-4 | Asbolute duality-gap stopping criterion of the solver.
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| eps_duality_gap_rel | 0 | Relative duality-gap stopping criterion of the solver.
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