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43
Convex programming methods for global optimization
 in COCOS
, 2003
"... Abstract. We investigate some approaches to solving nonconvex global optimization problems by convex nonlinear programming methods. We assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We pro ..."
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Cited by 3 (1 self)
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provide a survey of disjunctive programming with convex relaxations, logicbased outer approximation, and logicbased Benders decomposition. We then introduce a branchandbound method with convex quasirelaxations (BBCQ) that can be effective when the discrete variables take a large number of real values
LogicBased Methods for Global Optimization
, 2003
"... Logicbased methods provide a strategy for applying convex nonlinear programming to nonconvex global optimization. Such methods assume that the problem becomes convex when selected variables are fixed. The selected variables must be discrete, or else discretized if they are continuous. We provide a ..."
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tutorial survey of disjunctive programming with convex relaxations, logicbased outer approximation, and logicbased Benders decomposition. We then introduce a branchandbound method with convex quasirelaxations (BBCQ) that can be effective when the discrete variables take a large number of real values
Convex Boundary Angle
, 2003
"... Angle Based Flattening is a robust parameterization method that finds a quasiconformal mapping by solving a nonlinear optimization problem. We take advantage of a characterization of convex planar drawings of triconnected graphs to introduce new boundary constraints. This prevents boundary interse ..."
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Angle Based Flattening is a robust parameterization method that finds a quasiconformal mapping by solving a nonlinear optimization problem. We take advantage of a characterization of convex planar drawings of triconnected graphs to introduce new boundary constraints. This prevents boundary
A quasiconvex optimization approach to parameterized model order reduction
 In IEEE Proc. on Design Automation Conference
, 2005
"... Abstract—In this paper, an optimizationbased model order reduction (MOR) framework is proposed. The method involves setting up a quasiconvex program that solves a relaxation of the optimal H ∞ norm MOR problem. The method can generate guaranteed stable and passive reduced models and is very flexi ..."
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Cited by 32 (5 self)
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Abstract—In this paper, an optimizationbased model order reduction (MOR) framework is proposed. The method involves setting up a quasiconvex program that solves a relaxation of the optimal H ∞ norm MOR problem. The method can generate guaranteed stable and passive reduced models and is very
Convex relaxation of mixture regression with efficient algorithms
 In Advances in Neural Information Processing Systems
, 2010
"... We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations t ..."
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Cited by 2 (0 self)
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We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations
Strong Convergence in Stabilised Degenerate Convex Problems∗
"... Solutions to nonconvex variational problems typically exhibit enforced finer and finer oscillations called microstructures such that the infimal energy is not attained. Those oscillations are physically meaningful, but finite element approximations typically experience dramatic difficulty in their ..."
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in their reproduction. The relaxation of the nonconvex minimisation problem by (semi)convexification leads to a macroscopic model for the effective energy. The resulting discrete macroscopic problem is degenerate in the sense that it is convex but not strictly convex. This paper discusses a modified discretisation
Nonconvex Power Allocation Games in MIMO Cognitive Radio Networks
"... Abstract—We consider a sensingbased spectrum sharing scenario in a MIMO cognitive radio network where the overall objective is to maximize the total throughput of each cognitive radio user by jointly optimizing both the detection operation and the power allocation over all the channels, under a in ..."
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interference constraint bound to primary users. The resulting optimization problems lead to a nonconvex game, which presents a new challenge when analyzing the equilibria of this game. In order to deal with the nonconvexity of the game, we use a new relaxed equilibria concept, namely, quasiNash equilibrium
Blind Separation of QuasiStationary Sources: Exploiting Convex Geometry in Covariance Domain
, 2015
"... This paper revisits blind source separation of instantaneously mixed quasistationary sources (BSSQSS), motivated by the observation that in certain applications (e.g., speech) there exist time frames during which only one source is active, or locally dominant. Combined with nonnegativity of sourc ..."
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Cited by 3 (3 self)
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This paper revisits blind source separation of instantaneously mixed quasistationary sources (BSSQSS), motivated by the observation that in certain applications (e.g., speech) there exist time frames during which only one source is active, or locally dominant. Combined with nonnegativity
Maximizing Sum Rates in Cognitive Radio Networks: Convex Relaxation and Global Optimization Algorithms
"... Abstract—A key challenge in wireless cognitive radio networks is to maximize the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. We study the weighted sum rate maximiza ..."
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Cited by 6 (3 self)
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problem is established. In the general case, we propose a global optimization algorithm by utilizing our convex relaxation and branchandbound to compute an optimal solution. Our technique exploits the nonnegativity of the physical quantities, e.g., channel parameters, powers and rates, that enables key
Quality of service and maxminfair transmit beamforming to multiple cochannel multicast groups
 IEEE Trans. Signal Processing
, 2008
"... Abstract—The problem of transmit beamforming to multiple cochannel multicast groups is considered, when the channel state is known at the transmitter and from two viewpoints: minimizing total transmission power while guaranteeing a prescribed minimum signaltointerferenceplusnoise ratio (SINR) at ..."
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Cited by 38 (8 self)
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quasioptimal solutions. It is shown that Lagrangian relaxation coupled with suitable randomization/cochannel multicast power control yield computationally efficient highquality approximate solutions. For a significant fraction of problem instances, the solutions generated this way are exactly optimal
Results 1  10
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