This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP to ensure the exact recovery of every block $s$-sparse signal … Read more
In this work we study the p-median problem with maximum distance constraints (PMPDC) which is a variant of the classical p-median problem (PMP). First of all, we provide some different formulations for (PMPDC) because the heuristics procedures for the (PMPDC) with a formulation based on the approach that modifies the distance matrix that leads to … Read more
We give safe screening rules to eliminate variables from regression with L0 regularization or cardinality constraint. These rules are based on guarantees that a feature may or may not be selected in an optimal solution. The screening rules can be computed from a convex relaxation solution in linear time, without solving the L0 optimization problem. … Read more
We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, … Read more
This paper proposes an optimization framework for retailers that are involved in demand response (DR) programs. In a first phase responsive users optimize their own household consumption, characterizing not only their appliances and equipment but also their comfort preferences. Then, the retailer exploits in a second phase this preliminary non-coordinated solution to implement a strategy … Read more
Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more effective the tighter the used relaxations are. Relaxations are commonly established by convex underestimators, where each … Read more
A frequent challenge encountered by manufacturers of mechanical assemblies consists of the definition of quality criteria for the assembly lines of the subcomponents which are mounted into the final product. The rollout of Industry 4.0 standards paves the way for the usage of data-driven, intelligent approaches towards this goal. In this work, we investigate such … Read more
In this paper, we develop a Monte-Carlo based heuristic approach to approximate the objective function in long horizon optimal control problems. In this approach, we evolve the system state over multiple trajectories into the future while sampling the noise disturbances at each time-step, and find the weighted average of the costs along all the trajectories. … Read more
In the absence of direct demand-side bids for certain reliability products in the wholesale electricity markets, Independent System Operators (ISOs) traditionally use fixed demand requirements with penalty factors to clear the market. This approach does not allow proper tradeoffs between reliability and cost due to the inelasticity of the fixed requirements. Therefore, ISOs have been … Read more
Updating the augmented Lagrangian multiplier by closed-form expression yields efficient first-order infeasible approach for optimization problems with orthogonality constraints. Hence, parallelization becomes tractable in solving this type of problems. Inspired by this closed-form updating scheme, we propose an exact penalty function model with compact convex constraints (PenC). We show that PenC can act as an … Read more