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The application of semidefinite programming for detection in CDMA
 IEEE Journal on Selected Areas in Communications
, 2001
"... Abstract—In this paper, a detection strategy based on a semidefinite relaxation of the CDMA maximumlikelihood (ML) problem is investigated. Cutting planes are introduced to strengthen the approximation. The semidefinite program arising from the relaxation can be solved efficiently using interior ..."
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Cited by 42 (1 self)
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Abstract—In this paper, a detection strategy based on a semidefinite relaxation of the CDMA maximumlikelihood (ML) problem is investigated. Cutting planes are introduced to strengthen the approximation. The semidefinite program arising from the relaxation can be solved efficiently using interior point methods. These interior point methods have polynomial computational complexity in the number of users. The simulated bit error rate performance demonstrates that this approach provides a good approximation to the ML performance. Index Terms—Codedivision multiple access, multiuser detection, semidefinite programming. I.
Strong Duality and Minimal Representations for Cone Optimization
, 2008
"... The elegant results for strong duality and strict complementarity for linear programming, LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primaldual optimal pair that satisfies strict complementarity. This failure is ..."
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Cited by 13 (2 self)
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The elegant results for strong duality and strict complementarity for linear programming, LP, can fail for cone programming over nonpolyhedral cones. One can have: unattained optimal values; nonzero duality gaps; and no primaldual optimal pair that satisfies strict complementarity. This failure is tied to the nonclosure of sums of nonpolyhedral closed cones. We take a fresh look at known and new results for duality, optimality, constraint qualifications, and strict complementarity, for linear cone optimization problems in finite dimensions. These results include: weakest and universal constraint qualifications, CQs; duality and characterizations of optimality that hold without any CQ; geometry of nice and devious cones; the geometric relationships between zero duality gaps, strict complementarity, and the facial structure of cones; and, the connection between theory and empirical evidence for lack of a CQand failure of strict complementarity. One theme is the notion of minimal representation of the cone and the constraints in order to regularize the problem and avoid both the theoretical and numerical difficulties that arise due to (near) loss of a CQ. We include a discussion on obtaining these representations efficiently.
Semirandom Models as Benchmarks for Coloring Algorithms
"... Semirandom models generate problem instances by blending random and adversarial decisions, thus intermediating between the worstcase assumptions that may be overly pessimistic in many situations, and the easy pure random case. In the Gn,p,k random graph model, the n vertices are partitioned into k ..."
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Cited by 7 (2 self)
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Semirandom models generate problem instances by blending random and adversarial decisions, thus intermediating between the worstcase assumptions that may be overly pessimistic in many situations, and the easy pure random case. In the Gn,p,k random graph model, the n vertices are partitioned into k color classes each of size n/k. Then, every edge connecting two different color classes is included with probability p = p(n). In the semirandom variant, G ∗ n,p,k, an adversary may add edges as long as the planted coloring is respected. Feige and Killian prove that unless NP ⊆ BP P, no polynomial time algorithm works whp when np < (1 − ɛ) ln n, in particular when np is constant. Therefore, it seems like G ∗ n,p,k is not an interesting benchmark for polynomial time algorithms designed to work whp on sparse instances (np a constant). We suggest two new criteria, using semirandom models, to serve as benchmarks for such algorithms. We also suggest two new coloring heuristics and compare them with the coloring heuristics suggested by Alon and Kahale 1997 and by Böttcher 2005. We prove that in some explicit sense both our heuristics are preferable to the latter.
Robust Farkas’ lemma for uncertain linear systems with applications
 Positivity, DOI
"... We present a robust Farkas lemma, which provides a new generalization of the celebrated Farkas lemma for linear inequality systems to uncertain conical linear systems. We also characterize the robust Farkas lemma in terms of a generalized characteristic cone. As an application of the robust Farkas l ..."
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Cited by 4 (4 self)
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We present a robust Farkas lemma, which provides a new generalization of the celebrated Farkas lemma for linear inequality systems to uncertain conical linear systems. We also characterize the robust Farkas lemma in terms of a generalized characteristic cone. As an application of the robust Farkas lemma we establish a characterization of uncertaintyimmunized solutions of conical linear programming problems under uncertainty. AMS Subject Classifications: 90C30, 49B27, 90C48 1
A Revisit to Quadratic Programming with One Inequality Quadratic Constraint via Matrix Pencil ∗
, 2013
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Global Optimization of Robust Truss Topology via Mixed Integer Semidefinite Programming
, 2009
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Semidefinite relaxations for integer programming
, 2009
"... We survey some recent developments in the area of semidefinite optimization applied to integer programming. After recalling some generic modeling techniques to obtain semidefinite relaxations for NPhard problems, we look at the theoretical power of semidefinite optimization in the context of the Ma ..."
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Cited by 1 (0 self)
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We survey some recent developments in the area of semidefinite optimization applied to integer programming. After recalling some generic modeling techniques to obtain semidefinite relaxations for NPhard problems, we look at the theoretical power of semidefinite optimization in the context of the MaxCut and the Coloring Problem. In the second part, we consider algorithmic questions related to semidefinite optimization, and point to some recent ideas to handle large scale problems. The survey is concluded with some more advanced modeling techniques, based on matrix relaxations leading to copositive matrices.
Assessing the Vulnerability of Replicated Network Services
"... Clientserver networks are pervasive, fundamental, and include such key networks as the Internet, power grids, and road networks. In a clientserver network, clients obtain a service by connecting to one of a redundant set of servers. These networks are vulnerable to node and link failures, causing ..."
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Clientserver networks are pervasive, fundamental, and include such key networks as the Internet, power grids, and road networks. In a clientserver network, clients obtain a service by connecting to one of a redundant set of servers. These networks are vulnerable to node and link failures, causing some clients to become disconnected from the servers. We develop algorithms that quantify and bound the inherent vulnerability of a clientserver network using semidefinite programming (SDP) and branchandcut techniques. Further, we develop a divideandconquer algorithm that solves the problem for large graphs. We use these techniques to show that: for the Philippine Power Grid removing just over 6 % of the transmission lines will disconnect at least 20 % but not more than 50 % of the substations from all generators; on a large wireless mesh network disrupting 5 % of wireless links between relays removes Internet access for half the relays; even after any 16 % of Tier 2 ASes are removed, more than 50 % of the remaining Tier 2 ASes will be connected to the Tier 1 backbone; when 300 roadblocks are erected in Michigan, it’s possible to disconnect 28–43% of the population from all airports. 1.