In this paper, we consider the joint design of both transmit waveforms and receive filters for a colocated multiple-input-multiple-output (MIMO) radar with the existence of signal-dependent interference and white noise. The design problem is formulated into a maximization of the signal-to-interference-plus-noise ratio (SINR), including various constraints on the transmit waveforms. Compared with the traditional alternating semidefinite relaxation approach, a general and flexible algorithm is proposed based on the majorization-minimization method with guaranteed monotonicity, lower computational complexity per iteration and/or convergence to a B-stationary point. Many waveform constraints can be flexibly incorporated into the algorithm with only a few modifications. Furthermore, the connection between the proposed algorithm and the alternating optimization approach is revealed. Finally, the proposed algorithm is evaluated via numerical experiments in terms of SINR performance, ambiguity function, computational time, and properties of the designed waveforms. The experiment results show that the proposed algorithms are faster in terms of running time and meanwhile achieve as good SINR performance as the the existing methods.

Transmit Waveform/Receive Filter Design for MIMO Radar With Multiple Waveform Constraints

https://www.duo.uio.no/bitstream/handle/10852/10532/pm03-06.pdf?sequence=1

A tensor product matrix approximation problem in quantum physics

Collaboration of networked microgrids (NMGs) with diverse generation sources is a promising solution to smooth volatile generation output and enhance the utilization efficiency of renewable energies. In addition to centralized and decentralized collaboration mechanisms, transactive energy control (TEC) is an emerging and effective market-based control to enable energy transactions among distributed entities such as NMGs. However, existing studies on TEC suffer from several major weaknesses such as unconstrained/simplified model formulations and slow convergence rates. This paper proposes a novel TEC mechanism to tackle these weaknesses. First, the centralized mechanism, decentralized mechanism, and subgradient-based TEC mechanism to coordinate the operation of NMGs are briefly reviewed and modeled by a scenario-based stochastic optimization method. A new TEC mechanism is then proposed, consisting of a TEC framework, mathematical model, pricing rule, and algorithm. The optimality of the proposed TEC mathematical model and pricing rule is demonstrated. The effectiveness of the proposed TEC mechanism is verified in case- studies where the NMGs operate in grid-connected, islanded, and congested modes. The advantages of the proposed TEC mechanism are also illustrated through comparisons with the centralized mechanism, decentralized mechanism, and subgradient-based TEC mechanism.

A Novel Transactive Energy Control Mechanism for Collaborative Networked Microgrids

In this work, we propose an inexact projected gradient-like method for solving smooth constrained vector optimization problems. In the unconstrained case, we retrieve the steepest descent method introduced by Grana Drummond and Svaiter. In the constrained setting, the method we present extends the exact one proposed by Grana Drummond and Iusem, since it admits relative errors on the search directions. At each iteration, a decrease of the objective value is obtained by means of an Armijo-like rule. The convergence results of this new method extend those obtained by Fukuda and Grana Drummond for the exact version. For partial orders induced by both pointed and nonpointed cones, under some reasonable hypotheses, global convergence to weakly efficient points of all sequences generated by the inexact projected gradient method is established for convex (respect to the ordering cone) objective functions. In the convergence analysis we also establish a connection between the so-called weighting method and the one we propose.

http://www.optimization-online.org/DB_FILE/2011/06/3062.pdf

Inexact projected gradient method for vector optimization

We present a rigorous and comprehensive survey on extensions to the multicriteria setting of three well-known scalar optimization algorithms. Multiobjective versions of the steepest descent, the projected gradient and the Newton methods are analyzed in detail. At each iteration, the search directions of these methods are computed by solving real-valued optimization problems and, in order to guarantee an adequate objective value decrease, Armijo-like rules are implemented by means of a backtracking procedure. Under standard assumptions, convergence to Pareto (weak Pareto) optima is established. For the Newton method, superlinear convergence is proved and, assuming Lipschitz continuity of the objectives second derivatives, it is shown that the rate is quadratic

/pdf/a-survey-on-multiobjective-descent-methods-2hrjjouog6.pdf

A survey on multiobjective descent methods

6.253 Convex Analysis and Optimization, Spring 2004

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6.253 Convex Analysis and Optimization, Spring 2004