    \begin{algorithmic}
    \Require Time limit of each subproblem $g_i(x,\lambda)$ (e.g., 10 sec.) 
    \State 
    $S \gets \{1,\cdots, N\}$
    \While{\texttt{!cut\_added}}
    
    \For{$i$ in $S$}    
        \State Solve $g_i(x,\lambda)$; $\texttt{TS}_i$ $\gets$ termination status of $g_i(x,\lambda)$
        \If{$\texttt{TS}_i = \texttt{OPTIMAL}$}
        \State Lines 19-23 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
        \ElsIf{$\texttt{TS}_i = \texttt{INFEASIBLE}$} 
            \State $S \gets S \setminus \{i\}$
        \ElsIf{$\texttt{TS}_i = \texttt{UNBOUNDED}$} 
        \State Lines 25-31 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
        \ElsIf{$\texttt{TS}_i$ = \texttt{TIME LIMIT}}
        \If{$g(x,\lambda)$ has a solution}
            \State Lines 19-23 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
        \EndIf
        \EndIf
    \EndFor
    \If{$S=\emptyset$} 
    \State $\texttt{UB} \gets v^\texttt{k}$; $\texttt{progressed} \gets \texttt{true}$
    \EndIf 
    \EndWhile
\end{algorithmic}

\begin{algorithmic}
\Require Time limit of each subproblem $g_i(x,\lambda)$ (e.g., 10 sec.)
\State
$S \gets \{1,\cdots, N\}$
\While{\texttt{!cut\_added}}
\For{$i$ in $S$}
\State Solve $g_i(x,\lambda)$; $\texttt{TS}_i$ $\gets$ termination status of $g_i(x,\lambda)$
\If{$\texttt{TS}_i = \texttt{OPTIMAL}$}
\State Lines 19-23 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
\ElsIf{$\texttt{TS}_i = \texttt{INFEASIBLE}$}
\State $S \gets S \setminus \{i\}$
\ElsIf{$\texttt{TS}_i = \texttt{UNBOUNDED}$}
\State Lines 25-31 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
\ElsIf{$\texttt{TS}_i$ = \texttt{TIME LIMIT}}
\If{$g(x,\lambda)$ has a solution}
\State Lines 19-23 of Algorithm \ref{algo}; %$\texttt{progressed} \gets \texttt{true}$
\EndIf
\EndIf
\EndFor
\If{$S=\emptyset$}
\State $\texttt{UB} \gets v^\texttt{k}$; $\texttt{progressed} \gets \texttt{true}$
\EndIf
\EndWhile
\end{algorithmic}
{
    "title": "two-stage distributionally robust conic linear programming over   1-wasserstein balls",
    "id": "2211.05903",
    "abstract": "this paper studies two-stage distributionally robust conic linear programming under constraint uncertainty over type-1 wasserstein balls. we present optimality conditions for the dual of the worst-case expectation problem, which characterizes worst-case uncertain parameters for its inner maximization problem. this condition offers an alternative proof, a counter-example, and an extension to previous works. additionally, the condition highlights the potential advantage of a specific distance metric for out-of-sample performance, as exemplified in a numerical study on a facility location problem with demand uncertainty. a cutting-plane-based algorithm and a variety of algorithmic enhancements are proposed with a finite convergence proof under less stringent assumptions.",
    "categories": "math.oc",
    "doi": "",
    "created": "2022-11-10",
    "updated": "2024-02-02",
    "authors": [
        "geunyeong byeon",
        "kaiwen fang",
        "kibaek kim"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2211.05903"
}
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