Non-Linear Programming

TL;DR: This paper proposes to resolve conflicts among multiple sources of heterogeneous data types by using an optimization framework where truths and source reliability are defined as two sets of unknown variables and the objective is to minimize the overall weighted deviation between the truths and the multi-source observations.

TL;DR: This survey focuses on providing a comprehensive overview of truth discovery methods, and summarizing them from different aspects, and offers some guidelines on how to apply these approaches in application domains.

TL;DR: Several truth discovery methods have been proposed for various scenarios, and they have been successfully applied in diverse application domains as discussed by the authors. But for the same object, there usually exist conflicts among the collected multi-source information.

TL;DR: This work investigates the temporal relations among both object truths and source reliability, and proposes an incremental truth discovery framework that can dynamically update object truth and source weights upon the arrival of new data.

TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).

Abstract: FOUNDATIONS. The Scope of Integer and Combinatorial Optimization. Linear Programming. Graphs and Networks. Polyhedral Theory. Computational Complexity. Polynomial-Time Algorithms for Linear Programming. Integer Lattices. GENERAL INTEGER PROGRAMMING. The Theory of Valid Inequalities. Strong Valid Inequalities and Facets for Structured Integer Programs. Duality and Relaxation. General Algorithms. Special-Purpose Algorithms. Applications of Special- Purpose Algorithms. COMBINATORIAL OPTIMIZATION. Integral Polyhedra. Matching. Matroid and Submodular Function Optimization. References. Indexes.

TL;DR: The algorithm consists of repeated application of such projective transformations each followed by optimization over an inscribed sphere to create a sequence of points which converges to the optimal solution in polynomial-time.

TL;DR: In this paper, the authors present a model-based approach to solving linear programming problems, which is based on the Gauss-Jordan method for solving systems of linear equations, and the Branch-and-Bound method for solving mixed integer programming problems.