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Semidefinite Relaxation of Quadratic Optimization Problems
In this article, we have provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope of applicability to key theoretical results. We have also showcased
Linear and Nonlinear Programming
TLDR
This new edition covers the central concepts of practical optimization techniques, with an emphasis on methods that are both state-of-the-art and popular, and the proof of the convergence property for both standard and accelerated steepest descent methods are presented in Chapter 8.
Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems
TLDR
This paper proposes a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix) and demonstrates that for a wide range of cost functions the associated distributionally robust stochastic program can be solved efficiently.
Disciplined Convex Programming
A new methodology for constructing convex optimization models called disciplined convex programming is introduced. The methodology enforces a set of conventions upon the models constructed, in turn
Semidefinite Programming Approaches for Sensor Network Localization With Noisy Distance Measurements
TLDR
An algorithm is described that solves the sensor network localization problem using advanced optimization techniques and the effect of using very noisy measurements is studied and robust methods to deal with high noise are proposed.
Statistical ranking and combinatorial Hodge theory
TLDR
Hodge decomposition sheds light on whether a given dataset may be globally ranked in a meaningful way or if the data is inherently inconsistent and thus could not have any reasonable global ranking; in the latter case it provides information on the nature of the inconsistencies.
Semidefinite programming based algorithms for sensor network localization
TLDR
An SDP relaxation based method is developed to solve the localization problem in sensor networks using incomplete and inaccurate distance information and an iterative distributed SDP method for solving very large scale semidefinite programs that arise out of localization problems for large dense networks and are intractable using centralized methods.
Interior point algorithms - theory and analysis
  • Y. Ye
  • Computer Science
    Wiley-Interscience series in discrete mathematics…
  • 5 August 1997
TLDR
This paper presents a meta-analyses of Linear Programming Algorithms and its applications to Convex Optimization, focusing on the areas of linear programming and nonconvex optimization.
Approximation Algorithms for Metric Facility Location Problems
TLDR
This paper presents a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and a soft-capacitate facility location algorithm that achieves the integrality gap of the standard linear programming relaxation of the problem.
Theory of semidefinite programming for Sensor Network Localization
TLDR
It is shown, for the first time, that these networks can be localized in polynomial time and a notion called strong localizability is introduced and shown that the SDP model will identify all strongly localizable sub-networks in the input network.
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