In this article, we have provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope applicability to key theoretical results. We also showcased several representative applications, namely MIMO detection, B¿ shimming in MRI, sensor network localization. Another important application, downlink transmit beamforming, is described [1]. Due space limitations, are unable cover many other beautiful applications although done our best illustrate intuitive...

Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution be misleading when there is ambiguity the choice of a distribution for random parameters. this paper, we propose model that describes uncertainty both form (discrete, Gaussian, exponential, etc.) and moments (mean covariance matrix). We demonstrate wide range cost functions associated...

We describe an SDP relaxation based method for the position estimation problem in wireless sensor networks. The optimization is set up so as to minimize error positions fit distance measures. Observable gauges are developed check quality of point sensors or detect erroneous sensors. performance this technique highly satisfactory compared other techniques. Very few anchor nodes required accurately estimate all unknown a network. Also errors minimal even when not suitably placed within network...

An SDP relaxation based method is developed to solve the localization problem in sensor networks using incomplete and inaccurate distance information. The set up find a of positions such that given constraints are satisfied. nonconvex formulation then relaxed order yield semidefinite program can be solved efficiently.The basic model extended account for noisy In particular, maximum likelihood an interval discussed. solution also used as starting point steepest descent local optimization...

We describe several adaptive-step primal-dual interior point algorithms for linear programming. All have polynomial time complexity while some allow very long steps in favorable circumstances. provide heuristic reasoning expecting that the will perform much better practice than guaranteed by worst-case estimates, based on an analysis using a nonrigorous probabilistic assumption.

We propose a technique that we call HodgeRank for ranking data may be incomplete and imbalanced, characteristics common in modern datasets coming from e-commerce internet applications. are primarily interested cardinal based on scores or ratings though our methods also give specific insights ordinal data. From raw data, construct pairwise rankings, represented as edge flows an appropriate graph. Our statistical method exploits the graph Helmholtzian, which is theoretic analogue of Helmholtz...

Recently, variable selection and sparse reconstruction are solved by finding an optimal solution of a minimization model, where the objective function is sum data-fitting term in $\ell_2$ norm regularization $\ell_p$ $(0<p<1)$. Since it nonconvex most algorithms for solving problem can provide only approximate local solution, nonzero entries cannot be identified theoretically. In this paper, we establish lower bounds absolute value every which used to indentify zero precisely any numerical...

A natural optimization model that formulates many online resource allocation problems is the linear programming (LP) problem in which constraint matrix revealed column by along with corresponding objective coefficient. In such a model, decision variable has to be set each time without observing future inputs, and goal maximize overall function. this paper, we propose near-optimal algorithm for general class of under assumptions random order arrival some mild conditions on size LP...

We present an O(√nL)-iteration homogeneous and self-dual linear programming (LP) algorithm. The algorithm possesses the following features: • It solves problem without any regularity assumption concerning existence of optimal, feasible, or interior feasible solutions. can start at positive primal-dual pair, infeasible, near central ray orthant (cone), it does not use big M penalty parameter lower bound. Each iteration a system equations whose dimension is almost same as that solved in...

We present a dual-scaling interior-point algorithm and show how it exploits the structure sparsity of some large-scale problems. solve positive semidefinite relaxation combinatorial quadratic optimization problems subject to boolean constraints. report first computational results algorithms for approximating maximum cut programs with dimension up 3,000.

In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed the case in which constraints are two inequalities. This formulation termed extended trust region subproblem paper, to distinguish it from ordinary subproblem, constraint a single ellipsoid. computational complexity of general still unknown. consider interesting cases related problem and show that for those corresponding semidefinite...

In this paper we present a 1.52-approximation algorithm for the metric uncapacitated facility location problem, and 2-approximation capacitated problem with soft capacities. Both these algorithms improve best previously known approximation factor corresponding our soft-capacitated achieves integrality gap of standard linear programming relaxation problem. Furthermore, will show, using result Thorup, that can be implemented in quasi-linear time.

We consider a retailer selling single product with limited on-hand inventory over finite season. Customer demand arrives according to Poisson process, the rate of which is influenced by action taken (such as price adjustment, sales commission, advertisement intensity, etc.). The relationship between and not known in advance. However, able learn optimal on fly she maximizes her total expected revenue based observed reactions. Using pricing problem an example, we propose dynamic...