From 7dfcc480ba1e19bd3232349fc733caef94034292 Mon Sep 17 00:00:00 2001
From: stainer_t <thomas.stainer@oecd-nea.org>
Date: Mon, 8 Sep 2025 13:48:49 +0200
Subject: Initial commit from Polytechnique Montreal

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+\subsection{Contents of a \dir{optimize} data structure}
+
+The \dir{optimize} specification is used to store the optimization variables and functions values and definitions, limits and
+options.
+
+\vskip 0.08cm
+
+In any case, the signature variable for this data structure must be $\mathsf{SIGNA}$=\verb*|L_OPTIMIZE  |. The dimensioning
+parameters for this data structure, which are stored in the state vector $\mathcal{S}^{o}_{i}$, represents:
+
+\begin{itemize}
+\item The number of decision variables $N_{var} = \mathcal{S}^{o}_{1}$.
+\item The number of constraints $N_{cst} = \mathcal{S}^{o}_{2}$.
+\item The type of optimization  $\mathcal{S}^{o}_{3}$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{3} = \left\{
+\begin{array}{rl}
+ 1 & \textrm{minimization} \\
+ -1 & \textrm{maximization} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The result of a test for external convergence of the optimization problem $\mathcal{S}^{o}_{4}$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{4} = \left\{
+\begin{array}{rl}
+ 0 & \textrm{not converged} \\
+ 1 & \textrm{converged} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The index of external iteration (${S}^{o}_{5}$). If module {\tt PLQ:} is used, this is the iteration index relative to
+the solution of a new linear optimization problem with a quadratic constraint. If module {\tt LNSR:} is used, this is the number
+of times the line search algorithm is called.
+
+\item The type of reduction for the radius if the quadratic constraint ($\mathcal{S}^{o}_{6}$) used in module {\tt PLQ:}, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{6} = \left\{
+\begin{array}{rl}
+ 1 & \textrm{half} \\
+ 2 & \textrm{parabolic} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The type of gradient search $\mathcal{S}^{o}_{7}$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{7} = \left\{
+\begin{array}{rl}
+ 0 & \textrm{steepest descent} \\
+ 1 & \textrm{conjugate gradient} \\
+ 2 & \textrm{Broyden-Fletcher-Goldfarb-Shanno (BFGS)} \\
+ 3 & \textrm{memory limited Broyden-Fletcher-Goldfarb-Shanno (LBFGS)} \\
+ 4 & \textrm{Newton method for unconstrained optimization} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The type of optimization method $\mathcal{S}^{o}_{8}$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{8} = \left\{
+\begin{array}{rl}
+ 0 & \textrm{not set} \\
+ 1 & \textrm{OPTEX method with module {\tt PLQ:}} \\
+ 2 & \textrm{line search algorithm with module {\tt LNSR:}} \\
+ 3 & \textrm{fixed point SPH algorithm with module {\tt FPSPH:}} \\
+ 4 & \textrm{Newtonian SPH algorithm with module {\tt FPSPH:}} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The resolution's method for the linear problem with quadratic constraint used in module {\tt PLQ:} ($\mathcal{S}^{o}_{9})$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{9} = \left\{
+\begin{array}{rl}
+ 1 & \textrm{SIMPLEX/LEMKE} \\
+ 2 & \textrm{LEMKE/LEMKE} \\
+ 3 & \textrm{MAP} \\
+ 4 & \textrm{Augmented Lagragian} \\
+ 5 & \textrm{Penalty Method} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The index of line search iteration in module {\tt LNSR:} (${S}^{o}_{10}$). The maximum number of line search iterations is fixed to 50 in module {\tt LNSR:}.
+
+\item The result of a test for the convergence of the line search iterations $\mathcal{S}^{o}_{11}$ in module {\tt LNSR:}, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{11} = \left\{
+\begin{array}{rl}
+ 0 & \textrm{not converged} \\
+ 1 & \textrm{converged} \\
+ 2 & \textrm{maximum line search iteration reached} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The maximum number of external iterations in module {\tt LNSR:} (${S}^{o}_{12}$).
+
+\item The external iteration restart cycle in module {\tt LNSR:} (${S}^{o}_{13}$).
+
+\item A flag for unsuccessful resolution in module {\tt PLQ:} ${S}^{o}_{14}$, where
+
+\begin{displaymath}
+\mathcal{S}^{o}_{14} = \left\{
+\begin{array}{rl}
+ 0 & \textrm{successful at last iteration} \\
+ \ge 1 & \textrm{number of iteration with unsuccessful resolution.} \\
+\end{array} \right.
+\end{displaymath}
+
+\end{itemize}
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{optimize}}{7.0cm}
+
+\CharEnr
+{SIGNATURE\blank{3}}{$*12$}
+{Signature of the data structure ($\mathsf{SIGNA}$)}
+
+\IntEnr
+{STATE-VECTOR}{$40$}
+{Vector describing the various parameters associated with data structure $\mathcal{S}^{o}_{i}$.}
+
+\OptIntEnr
+{DEL-STATE\blank{3}}{$40$}{*}
+{Vector describing the various parameters associated with data structure $\mathcal{S}^{g}_{i}$. This array is
+ available if the {\sc optimize} object has been created using module {\tt DLEAK:} or {\tt DSPH:}.}
+
+\DbleEnr
+{VAR-VALUE\blank{3}}{$N_{var}$}{}
+{The values of the decision variables}
+
+\DbleEnr
+{VAR-VAL-MAX\blank{1}}{$N_{var}$}{}
+{The maximum values of the decision variables can be.}
+
+\DbleEnr
+{VAR-VAL-MIN\blank{1}}{$N_{var}$}{}
+{The minimum values of the decision variables can be.}
+
+\DbleEnr
+{VAR-WEIGHT\blank{2}}{$N_{var}$}{}
+{The weight of the decision variables $w_{i}$ in the quadratic constraint.}
+
+\DbleEnr
+{CST-OBJ\blank{5}}{$N_{cst}$}{}
+{The limit value of the contraints. The units depends with the type of the constraint type.}
+
+\IntEnr
+{CST-TYPE\blank{4}}{$N_{cst}$}
+{The type of the contraints: =-1 for $\geq$; =0 for $=$; =1 for $\leq$.}
+
+\DbleEnr
+{CST-WEIGHT\blank{2}}{$N_{cst}$}{}
+{The weight of the constraint $\eta_{j}$ and $\gamma_{j}$ for the duals and meta-heuristic methods.}
+
+\DbleEnr
+{FOBJ-CST-VAL}{$N_{cst}+1$}{}
+{The actual values of the objective function (first value) and the contraints (the following values). The
+number of the constraints are assigned in the order they have been defined.}
+
+\DbleEnr
+{OPT-PARAM-R\blank{1}}{$40$}{}
+{The different limits and values for the iterative calculations of the optimization problem.}
+
+\DbleEnr
+{GRADIENT\blank{4}}{$N_{var}, N_{cst}+1$}{}
+{The gradients of the objective function and the constraints. The gradients of the objective for all the
+decision variables are in first position, then follow the gradients of the constraints.}
+
+\OptDbleEnr
+{GRADIENT-DIR}{$N_{var}, N_{cst}+1$}{*}{}
+{The direct component (without the flux effect) for the gradients of the objective function and the constraints.}
+
+\OptDbleEnr
+{DIRECTION\blank{3}}{$N_{var}$}{$\mathcal{S}^{o}_{8}=2$}{}
+{Direction of the line search.}
+
+\OptDbleEnr
+{HESSIAN\blank{5}}{$N_{var}, N_{var}$}{$\mathcal{S}^{o}_{7}=2$}{}
+{The hessian matrix containing second derivatives of the objective function with respect to the decision variables.}
+
+\OptDbleEnr
+{LNSR-INFO\blank{3}}{$9$}{$\mathcal{S}^{o}_{8}=2$}{}
+{Double precision values used by module {\tt LNSR:}.}
+
+\DirEnr
+{OLD-VALUE\blank{3}}
+{Directory containing differents informations of the previous iterations. the values of the decision
+variables, the objective function, the constraints and the gradients of these functions for the previous
+external iteration. This repertory will be created by the module \moc{PLQ:} (unless it is specified to not do) or by module \moc{LNSR:}.}
+
+\end{DescriptionEnregistrement}
+
+The array {\tt OPT-PARAM-R} contains double precision values related with the different limits and values for the iterative calculations of the optimization problem: \\
+\begin{tabular}{p{0.06\textwidth}p{0.1\textwidth}p{0.75\textwidth}}
+1st & $S$ & initial radius of the quadratic constraint in module {\tt PLQ:} or maximum stepsize for the line
+search in module {\moc LNSR:} (default: 1.0).\\
+2nd & $\delta$ & initial size of the hypercube for MAP method. (default: 0.1).\\
+3rd & $\varepsilon_{\rm ext}$ & limit for external convergence (default: $10^{-4}$).\\
+4th & $\varepsilon_{\rm int}$ & limit for internal convergence (default: $10^{-4}$).\\
+5th & $\varepsilon_{\rm quad}$ & limit for convergence of the quadratic constraint in module {\moc PLQ:} (default: $10^{-4}$). \\
+\end{tabular} \\
+The other value of the record are not used and set to 0.0.
+
+\vskip 0.2cm
+
+The optional array {\tt DEL-STATE} contains integer values related to the definition of mixture and group indices in module {\tt DLEAK:}.
+\begin{itemize}
+\item The number of energy groups in macrolib $\mathcal{S}^{g}_{1}$.
+\item The number of mixtures in macrolib $\mathcal{S}^{g}_{2}$.
+\item The type of leakage parameters $\mathcal{S}^{g}_{3}$,
+where
+\begin{displaymath}
+\mathcal{S}^{g}_{3} = \left\{
+\begin{array}{rl}
+1 & \textrm{use diffusion coefficients} \\
+2 & \textrm{use $P_1$-weighted macroscopic total cross sections.} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The type of control variables $\mathcal{S}^{g}_{4}$,
+where
+\begin{displaymath}
+\mathcal{S}^{g}_{4} = \left\{
+\begin{array}{rl}
+1 & \textrm{use leakage parameters} \\
+2 & \textrm{use correction factors on leakage parameters} \\
+3 & \textrm{use SPH factors compatible with diffusion theory, $P_n$ and $SP_n$ equations} \\
+4 & \textrm{use SPH factors compatible with other types of transport-theory macro-} \\
+& \textrm{calculations} \\
+5 & \textrm{use one SPH factor assigned to the albedo function in each macro-group.} \\
+\end{array} \right.
+\end{displaymath}
+
+\item The minimum group index $\mathcal{S}^{g}_{5}$, with $1 \le \mathcal{S}^{g}_{5}\le \mathcal{S}^{g}_{1}$.
+\item The maximum group index $\mathcal{S}^{g}_{6}$, with $\mathcal{S}^{g}_{5} \le \mathcal{S}^{g}_{6}\le \mathcal{S}^{g}_{2}$.
+\item The minimum mixture index $\mathcal{S}^{g}_{7}$, with $1 \le \mathcal{S}^{g}_{7}\le \mathcal{S}^{g}_{2}$.
+\item The maximum mixture index $\mathcal{S}^{g}_{8}$, with $\mathcal{S}^{g}_{7} \le \mathcal{S}^{g}_{8}\le \mathcal{S}^{g}_{2}$.
+\item The number of physical albedos $\mathcal{S}^{g}_{9}$.
+
+\end{itemize}
+\goodbreak
+
+\subsubsection{The sub-directory /OLD-VALUE/ in /optimize/}
+
+\begin{DescriptionEnregistrement}{Main records and sub-directories in \dir{/OLD-VALUE/}}{7.0cm}
+\DbleEnr
+{VAR-VALUE\blank{3}}{$N_{var}$}{}
+{The values of the decision variables of the last valid iteration.}
+
+\DbleEnr
+{FOBJ-CST-VAL}{$N_{cst}+1$}{}
+{The values of the objective function and the contraints of the last valid iteration.}
+
+\DbleEnr
+{GRADIENT\blank{4}}{$N_{var}, N_{cst}+1$}{}
+{The gradients of the objective function and the constraints of the last valid iteration.}
+
+\OptDbleEnr
+{VAR-VALUE2\blank{2}}{$N_{var}$}{$\mathcal{S}^{o}_{8}=1$}{}
+{The values of the decision variables of the second-last valid iteration.}
+
+\OptDbleEnr
+{BEST-VAR\blank{4}}{$N_{var}$}{$\mathcal{S}^{o}_{8}=1$}{}
+{The values of the decision variables corresponding to the best valid solution ever found.}
+
+\OptDbleEnr
+{BEST-FCT\blank{4}}{1}{$\mathcal{S}^{o}_{8}=1$}{}
+{The value of the objective function corresponding to the best valid solution ever found.}
+
+\end{DescriptionEnregistrement}
+\clearpage
+
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