Adjustable robust counterpart of conic quadratic problems

Oracle-based algorithms for binary two-stage robust optimization

“…For two-stage robust problems with non-linear robust constraints decision rules have been applied in [58,69]. The two-stage problem is studied for second order conic optimization problems in [28]. In [9,56] the authors derive robust counterparts of uncertain non-linear constraints.…”

Optimized dynamic policy for robust receding horizon control

“…However, while the policy in (2.42) leads to a non-convex control optimization problem in variables v(t + i|t) and K j (t + i|t), i = 0, .., N − 1, the disturbance-based policy (2.41), which parameterizes the control inputs as affine functions of only the uncertain quantities w(t + i), i = 1, .., N − 1, allows a convex optimization of the control inputs. The technique of optimizing the 'adjustable' decision variables parameterized as affine functions of uncertain parameters of the optimization problem has been explored in more general forms in the context of using adjustable robust counterparts of uncertain problems in the optimization literature (see, e.g., [118][119][120]). While the approach of optimizing future inputs or input perturbations as affine functions of previous disturbances gives less conservative results through the solution of an elegantly tractable problem, the on-line computational complexity is significantly high -at least of the order O(N 3 ) when solving a relevant quadratic optimization problem with the perturbations v(t + i|t) and gainsK j (t + i|t), i = 0, .., N − 1, j = 0, .., i − 1 as variables [121].…”

Two-Stage Robust Optimization Models for Power System Operation and Planning Under Joint Generation and Transmission Security Criteria

“…Therefore, the robust optimization framework based on bilevel programming of [10] and [11] is not readily applicable when the effect of the transmission network is accounted for. As a distinctive feature, the proposed approach is based on adjustable robust optimization (ARO) [41,42]. Similar to robust optimization, ARO is suitable to model optimization problems where the optimal solution must remain feasible for the worst-case parameter variation in a user-defined set, denoted as uncertainty set [24,37].…”

“…Similar to robust optimization, ARO is suitable to model optimization problems where the optimal solution must remain feasible for the worst-case parameter variation in a user-defined set, denoted as uncertainty set [24,37]. In contrast, ARO allows incorporating the flexibility of adjustable decisions, also known as recourse actions, in robust counterparts [41,42]. In this setting, ARO involves a trilevel optimization process [41][42][43].…”

“…In contrast, ARO allows incorporating the flexibility of adjustable decisions, also known as recourse actions, in robust counterparts [41,42]. In this setting, ARO involves a trilevel optimization process [41][42][43]. The upper level determines optimal non-adjustable decisions, i.e., decisions that must be feasible for every deviation of the uncertain parameters.…”