Simple and fast algorithm for binary integer and online linear programming

An Online Algorithm for Chance Constrained Resource Allocation

“…Recall that ( 4) is an ILP problem and Li et al [11] have proposed an effective OPD algorithm to solve the online ILP problem. For simplicity, denote ãtj = ātj + Φ −1 (ηj)γtj / √ n and we present the OPD method as shown in Algorithm 1.…”

“…The deterministic RAP can be modeled as a 0-1 integer linear programming (ILP) problem. Many recent papers have studied the online ILP problems (see [5][6][7][8][9][10][11][12][13] and references therein). Algorithms in [5][6][7][8][9][10][11][12][13] are all dual-based which maintain dual prices in iterations and can achieve near-optimal solutions under mild conditions.…”

“…Many recent papers have studied the online ILP problems (see [5][6][7][8][9][10][11][12][13] and references therein). Algorithms in [5][6][7][8][9][10][11][12][13] are all dual-based which maintain dual prices in iterations and can achieve near-optimal solutions under mild conditions. When a new request arrives, the decision is made immediately based on the dual price vector.…”

“…Among these studies, researchers [5][6][7][8][9] construct dual problems by using historical information and solving them to obtain the dual prices. To deal with the disadvantage that solving dual problems may be time-consuming, researchers [10][11][12][13] propose online primal-dual (OPD) algorithms that update the dual prices by utilizing the dual mirror descent or projected stochastic subgradient descent without solving optimization problems.…”

“…However, the optimization models studied in [5][6][7][8][9][10][11][12][13] are deterministic and may suffer from poor performance when the resource consumption is uncertain in practice. In the existing articles that study the uncertain online optimization, the uncertainty is modeled by the worst-case scenario value, expectation, regret, or a linear combination of the above (see [14][15][16][17][18]).…”