We present a survey of nondifferentiable optimization problems and methods with special focus on the analytic center cutting plane method. We propose a self-contained convergence analysis, that uses the formalism of the theory of self-concordant functions, but for the main results, we give direct proofs based on the properties of the logarithmic function. We also provide an in depth analysis of...

A general assumption made in evaluation of flow network reliability is perfectly reliable nodes. Under such assumption, network reliability is evaluated through subset cut or composite path set approaches. This paper presents a simple approach to account for node failures in reliability evaluation of flow networks using subset cut approach. The proposed approach starts with generating combinati...

Learning short binary codes is challenged by the inherent discrete nature of the problem. The graph cuts algorithm is a well-studied discrete label assignment solution in computer vision, but has not yet been applied to solve the binary coding problems. This is partially because it was unclear how to use it to learn the encoding (hashing) functions for out-of-sample generalization. In this pape...

A new cut elimination method is obtained here by “proof mining” (unwinding) from the following non-effective proof that begins with extracting an infinite branch B when the canonical search tree T for a given formula E of first order logic is not finite. The branch B determines a semivaluation so that B |= Ē and (*) every semivaluation can be extended to a total valuation. Since for every deriv...

This paper introduces a new cutting plane method for two-stage stochastic mixed-integer programming (SMIP) called Fenchel decomposition (FD). FD uses a class of valid inequalities termed, FD cuts, which are derived based on Fenchel cutting planes from integer programming. First, we derive FD cuts based on both the first and second-stage variables, and devise an FD algorithm for SMIP and establi...

We develop a method for computing facet-defining valid inequalities for any mixed-integer set PJ . While our practical implementation does not return only facet-defining inequalities, it is able to find a separating cut whenever one exists. The separator is not comparable in speed with the specific cutting-plane generators used in branch-and-cut solvers, but it is general-purpose. We can thus u...

This thesis focuses on the use of cutting-plane techniques to improve general-purpose mixed-integer linear programming solvers. The first topic covered here is a fast separation method for two-row cuts. Two-row cuts are intersection cuts from two rows of a simplex tableau describing the LP relaxation of the problem. These types of cuts recently garnered a lot of attention from the scientific co...