We study a hybrid MIP/CP solution approach in which CP is used for detecting infeasibilities and generating cuts within a branch-and-cut algorithm for MIP. Our framework applies to MIP problems augmented by monotone constraints that can be handled by CP. We illustrate our approach on a generic multiple machine scheduling problem, and compare it to other hybrid MIP/CP algorithms.

This paper addresses the need for nonlinear programming algorithms that provide fast local convergence guarantees no matter if a problem is feasible or infeasible. We present an active-set sequential quadratic programming method derived from an exact penalty approach that adjusts the penalty parameter appropriately to emphasize optimality over feasibility, or vice versa. Conditions are presente...

In many applications, ranking of decision making units (DMUs) is a problematic technical task procedure to decision makers in data envelopment analysis (DEA), especially when there are extremely efficient DMUs. In such cases, many DEA models may usually get the same efficiency score for different DMUs. Hence, there is a growing interest in ranking techniques yet. The purpose of this paper is ra...

Return-To-Scale (RTS) is a most important topic in DEA. Many methods are not obtained for estimating RTS in DEA, yet. In this paper has developed the Banker-Trall approach to identify situation for RTS for the BCC model "multiplier form" with virtual weight restrictions that are imposed to model by DM judgments. Imposing weight restrictions to DEA models often has created problem of infeasibili...

We study two issues on condition numbers for convex programs: one has to do with the growth of the condition numbers of the linear equations arising in interior-point algorithms; the other deals with solving conic systems and estimating their distance to infeasibility. These two issues share a common ground: the key tool for their development is a simple, novel perspective based on implicitly-d...

In this paper, we present the design of a simultaneous compensator for a segment of systems based on an interpolation method with stable polynomial interpolants. This problem leads to formulate conditions of polynomial divisibility in the case of the simultaneous control as a polynomial interpolation issue. The feasibility and infeasibility of the approach is also analyzed. Finally, an algorith...

We propose in this paper an inexact dual gradient algorithm based on augmented Lagrangian theory and inexact information for the values of dual function and its gradient. We study the computational complexity certification of the proposed method and we provide estimates on primal and dual suboptimality and also on primal infeasibility. We also discuss implementation aspects of the proposed algo...

We discuss the application of random projections to the fundamental problem of deciding whether a given point in a Euclidean space belongs to a given set. We show that, under a number of different assumptions, the feasibility and infeasibility of this problem are preserved with high probability when the problem data is projected to a lower dimensional space. Our results are applicable to any al...

Control Flow Graph (CFG) is a compact representation of all executable paths of a program and it is central to most program analyses. Unfortunately, the direct use of a CFG has two major sources of imprecision: (a) the existence of infeasible paths, and (b) the merging of states along incoming edges of a control-flow merge. Addressing these two problems is the path-sensitivity issue, and it is ...

Symbolic execution with interpolation has emerged as a powerful technique for software verification. Its performance heavily relies heavily on the quality of the computed “interpolants”, formulas which succinctly describe a generalization of the symbolic states proved so far. Symbolic execution by default is eager, that is, execution along a symbolic path stops the moment when infeasibility is ...