Download Convex Optimization in Signal Processing and Communications by Daniel P. Palomar, Yonina C. Eldar PDF

By Daniel P. Palomar, Yonina C. Eldar

Over the last 20 years there were major advances within the box of optimization. particularly, convex optimization has emerged as a robust sign processing instrument, and the range of functions maintains to develop swiftly. This booklet, written by means of a staff of prime specialists, units out the theoretical underpinnings of the topic and offers tutorials on quite a lot of convex optimization purposes. Emphasis all through is on state-of-the-art examine and on formulating difficulties in convex shape, making this a terrific textbook for complex graduate classes and an invaluable self-study consultant. themes coated variety from automated code iteration, graphical types, and gradient-based algorithms for sign restoration, to semidefinite programming (SDP) leisure and radar waveform layout through SDP. additionally it is blind resource separation for picture processing, strong broadband beamforming, allotted multi-agent optimization for networked platforms, cognitive radio structures through online game concept, and the variational inequality technique for Nash equilibrium options.

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Pistikopoulos, “The explicit linear quadratic regulator for constrained systems,” Automatica, vol. 38, no. 1, pp. 3–20, 2002. [25] C. V. Rao, S. J. Wright, and J. B. Rawlings, “Application of interior-point methods to model predictive control,” Journal of Optimization Theory and Applications, vol. 99, no. 3, pp. 723–57, 1998. References 37 [26] Y. Wang and S. Boyd, “Performance bounds for linear stochastic control,” working manuscript, 2008. [27] V. M. Zavala and L. T. Biegler, “The advanced-step NMPC controller: optimality, stability and robustness,” Automatica, 2007, submitted for publication.

Each line also has a maximum allowed input power: pjin ≤ Pjmax , j = 1, . . , m. At each node the total incoming power, from lines entering the node and a generator, if one is attached to the node, is converted and routed to the outgoing nodes, and to any attached loads. We assume the conversion has an efficiency ηi ∈ (0, 1). Thus we have ⎛ ⎞ pjout = ηi ⎝gi + li + j∈I (i) pjin ⎠ , i = 1, . . 7) j∈O (j) where li is the load power at node i, gi is the generator input power at node i, I(i) is the set of incoming edges to node i, and O(i) is the set of outgoing edges from node i.

We take li = 0 if i ∈ L, and gi = 0 if i ∈ G. In the problem of optimal generation and distribution, the node loads li are given; the goal is to find generator powers gi ≤ Gimax , and line power flows piin and pjout , that minimize the total generating cost, which we take to be a linear function of the powers, cT g. Here ci is the (positive) cost per watt for generator i. 7) 0 ≤ g ≤ G max 0 ≤ pin ≤ P max , 0 ≤ pout with variables gi , for i ∈ G; pin ∈ Rm , and pout ∈ Rm . 6) to the inequalities pjin ≥ pjout + j (pjin ), j = 1, .

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