In this paper we introduce the s-monotone index selection rules for the well-known crisscross method for solving the linear complementarity problem (LCP). Most LCP solution methods require a priori information about the properties of the input matrix. One of the most general matrix properties often required for finiteness of the pivot algorithms (or polynomial complexity … Read more
This paper studies an extended trust region subproblem (eTRS)in which the trust region intersects the unit ball with m linear inequality constraints. When m=0, m=1, or m=2 and the linear constraints are parallel, it is known that the eTRS optimal value equals the optimal value of a particular convex relaxation, which is solvable in polynomial … Read more
Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles … Read more
Power grid vulnerability is a major concern of modern society, and its protection problem is often formulated as a tri-level defender-attacker-defender model. However, this tri-level problem is compu- tationally challenging. In this paper, we design and implement a Column-and-Constraint Generation algorithm to derive its optimal solutions. Numerical results on an IEEE system show that: (i) … Read more
In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivative-free methods and we propose a new algorithm combining coordinate rotations with approximate simplex gradients. Through extensive numerical experimentation, we … Read more
The conceptions of optimizing a quantitative classification hierarchy and the criterion of informational optimality have been used for modeling universal accuracy classification scale. Proposed model is based on test uncertainty ratios determined in conformity with optimal levels of confidence in evaluating measurement uncertainty, as well as on the optimal classification structure. The author believes that … Read more
We introduce a natural abstraction of propositional proof systems that are based on cut- ting planes. This leads to a new class of proof systems that includes many well-known meth- ods, such as Gomory-Chvátal cuts, lift-and-project cuts, Sherali-Adams cuts, or split cuts. The rank of a proof system corresponds to the number of rounds that … Read more
We address the following generalization $P$ of the Lowner-John’s ellipsoid problem. Given a (non necessarily convex) compact set $K\subset R^n$ and an even integer $d, find an homogeneous polynomial $g$ of degree $d$ such that $K\subset G:=\{x:g(x)\leq1\}$ and $G$ has minimum volume among all such sets. We show that $P$ is a convex optimization problem … Read more
We show that there are 0-1 and unbounded knapsack polytopes with super-polynomial extension complexity. More specifically, for each n in N we exhibit 0-1 and unbounded knapsack polyhedra in dimension n with extension complexity \Omega(2^\sqrt{n}). ArticleDownload View PDF
We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow … Read more