We describe a procedure to reduce variable bounds in Mixed Integer Nonlinear Programming (MINLP) as well as Mixed Integer Linear Programming (MILP) problems. The procedure works by combining pairs of inequalities of a linear programming (LP) relaxation of the problem. This bound reduction technique extends the feasibility based bound reduction technique on linear functions, used in MINLP and MI...

We analyze perturbations of the right-hand side and the cost parameters in linear programming (LP) and semidefinite programming (SDP). We obtain tight bounds on the norm of the perturbations that allow interior-point methods to recover feasible and near-optimal solutions in a single interior-point iteration. For the unique, nondegenerate solution case in LP, we show that the bounds obtained usi...

We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on measures and its dual on continuous functions. Then we approximate the LP by a hierarchy of finitedimensional semidefinite programming (SDP) programs on moments of...

The last several years have seen an increasing interest in combining the models and methods of optimization with those of constraint programming. Integration of the two was initially impeded by their diierent cultural origins , one having developed largely in the operations research community and the other in the computer science and artiicial intelligence communities. The advantages of merger,...

Polyhedral compilers can perform complex loop optimizations that improve parallelism and cache behaviour of loops in the input program. These transformations result in significant performance gains on modern processors which have large compute power and deep memory hierarchies. The paper, Polyhedral Auto-transformation with No Integer Linear Programming, identifies issues that adversely affect ...

It has been shown that the problem of deterministically classifying constraints in semidefinite programming (SDP) is NP complete. An SDP is constructed that makes it possible to extend some constraint classification results from linear programming (LP) to SDP. Necessary and sufficient conditions for constraint classification, and ultimately, a deterministic method for detecting such are applied...

In this paper, we consider a routing problem related to the widely used Open Shortest Path First (OSPF) protocol. We address the special version of OSPF which requires unique and symmetrical paths. To solve this problem, we propose a hybrid approach which combines Constraint Programming (CP) and Linear Programming (LP). Our approach employs some new constraint with problem-specific filtering al...

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

Generating a set of combinatorial test cases for web application and development is very important. Linear programming (LP) is one of approaches to generating small combinatorial test suite. But, for software under test (SUT), the number of combinatorial test cases is often extremely large. If using LP to optimize test suite, the optimizing efficiency is low for the enormous size of LP variable...

Branch-and-price is a generalization of linear programming (LP) based branch-and-bound specifically designed to handle integer programming (IP) formulations that contain a huge number of variables. The basic idea of branch-and-price is simple. Columns are left out of the LP relaxation because there are too many columns to handle efficiently and most of them will have their associated variable e...