This paper is concerned with the cross-validation criterion for best subset selection in a linear regression model. In contrast with the use of statistical criteria (e.g., Mallows’ $C_p$, AIC, BIC, and various information criteria), the cross-validation only requires the mild assumptions, namely, samples are identically distributed, and training and validation samples are independent. For this … Read more
Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is … Read more
We present a framework to obtain valid inequalities for optimization problems constrained by a reverse convex set, which is defined as the set of points in a polyhedron that lie outside a given open convex set. We are particularly interested in cases where the closure of the convex set is either non-polyhedral, or is defined … Read more
The Quadratic Unconstrained Binary Optimization (QUBO) model has gained prominence in recent years with the discovery that it unifies a rich variety of combinatorial optimization problems. By its association with the Ising problem in physics, the QUBO model has emerged as an underpinning of the quantum computing area known as quantum annealing and has become … Read more
A system-interdiction problem can be modeled as a bilevel program in which the upper level models interdiction decisions and the lower level models system operation. This paper studies MILSIP, a mixed-integer linear system interdiction problem, which assumes binary interdiction decisions and models system operations through a mixed-integer linear program. To solve large-scale instances of MILSIP, … Read more
We describe strong convex valid inequalities for conic quadratic mixed 0-1 optimization. These inequalities can be utilized for solving numerous practical nonlinear discrete optimization problems from value-at-risk minimization to queueing system design, from robust interdiction to assortment optimization through appropriate conic quadratic mixed 0-1 relaxations. The inequalities exploit the submodularity of the binary restrictions and … Read more
The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure … Read more
We introduce the noncooperative fixed charge transportation problem (NFCTP), which is a game-theoretic extension of the fixed charge transportation problem. In the NFCTP, competing players solve coupled fixed charge transportation problems simultaneously. Three versions of the NFCTP are discussed and compared, which differ in their treatment of shared social costs. This may be used from … Read more
Large Neighborhood Search (LNS) heuristics are among the most powerful but also most expensive heuristics for mixed integer programs (MIP). Ideally, a solver learns adaptively which LNS heuristics work best for the MIP problem at hand in order to concentrate its limited computational budget. To this end, this work introduces Adaptive Large Neighborhood Search (ALNS) … Read more
Weighted or reweighted strategies have not been considered for sparsity constrained optimization. In this paper, we reformulate the sparsity constraint as an equivalent weighted l1-norm constraint in the sparsity constrained optimization problem. To solve the reformulated problem, we investigate the problem in the Lagrange dual framework, and prove that the strong duality property holds. Then … Read more