Second-order Cone Programming Techniques Research Articles

Bearing capacity of shallow strip foundations on reinforced soil subjected to combined loading using upper bound theorem of finite element limit analysis and second-order cone programming

Bearing capacity of shallow strip foundations placed over both unreinforced and reinforced granular soils and subjected to combined loading is calculated by implementation of upper bound finite element limit analysis in conjunction with second-order cone programming technique. The soil mass is considered to be a granular medium reinforced with the inclusion of horizontal single and double layers of geogrid elements. To represent the impact of tensile resistance of reinforcement elements, an axillary variable is utilized to simulate the plastic energy dissipation of reinforcing elements without the application of any stress variables. General loading conditions are considered to profile the expansion of the failure envelopes in the V-H and V-M spaces for shallow strip foundations resting on reinforced soils. Results of this study are compared and validated against three different cases including the bearing capacity of shallow strip foundations subjected to vertical loading in the case of perfectly smooth and fully rough interfaces, limit load of shallow strip foundations subjected to combined loading, and vertical bearing capacity of shallow strip footings over a soil deposit reinforced with a single-layer of geosynthetic. Consistency of the results with those reported in the literature demonstrates the efficiency of proposed extended finite element upper bound formulations. The results are reported in the form of an efficiency factor which can be multiplied by the vertical bearing capacity of the shallow strip footing over unreinforced soil to find the ultimate bearing capacity of the reinforced foundation. The results show that the load inclination angle and eccentricity have significant impacts on the limit load and the optimum embedment depths of the reinforcement layer. It is further noted that the effect of reinforcement layer(s) in the improvement of bearing capacity in the V-M space is more pronounced than in the V-H space. The efficiency of reinforcement elements inclusion in improving the expanse of safe loading domain in the V-H and V-M spaces enhances with an increase in the soil internal friction angle.

Secrecy Throughput Maximization for IRS-Aided MIMO Wireless Powered Communication Networks

In this paper, we consider deploying an intelligent reflecting surface (IRS) to enhance the downlink (DL) energy transfer and uplink (UL) information transmission efficiency for secure multiple-input multiple-output (MIMO) wireless powered communication networks (WPCNs). We aim to maximize the secrecy throughput of all users by jointly optimizing the DL/UL time allocation, the energy transmit covariance matrix of hybrid access point (AP), the information transmit beamforming matrix of users and the phase shifts of IRS in DL/UL, subject to constraints of energy/information transmit power at the hybrid AP/users and that of unit-modulus IRS phase shifts for DL/UL. To tackle the non-convex problem, we first transform the original problem into an equivalent form based on the mean-square error (MSE) method given time allocation, and then apply the alternating algorithm to update the optimization variables iteratively. Specifically, the energy covariance matrix and the information beamforming matrix are obtained based on the dual subgradient method. For the IRS phase shifts, we investigate two IRS beamforming reflection setups, namely different DL/UL IRS beamforming and identical DL/UL IRS beamforming. For the former case, the second-order cone programming technique and the Majorization-Minimization algorithm/element by element iterative algorithm are applied to obtain the DL and UL IRS phase shifts, respectively. For the latter case, the IRS phase shifts are obtained by the successive convex approximation technique. To further reduce the computational complexity of the single-user system, we derive the closed-form solutions of IRS phase shifts in each iteration for the two different reflection setups. Simulation results show that all the proposed algorithms can greatly improve the secrecy throughput compared to the conventional system without IRS.

Transmit power optimization over low-power Poisson channel in multiuser MISO indoor optical communications

Abstract In this paper, we address the problem of joint transmit beamforming and power control for a multiuser multiple-input single-output (MISO) indoor optical downlink channel. We adopt a shot-noise limited Poisson channel with transmitting signals subject to average and peak transmits power constraints. To minimize the total transmit power, we formulate an optimal downlink beamforming problem using convex optimization method via second-order cone programming techniques. In our approach, the total transmit power is optimized subject to the signal-to-interference-plus-noise ratio (SINR). The results verify performance improvements of the proposed technique as compared to conventional multiuser MISO indoor optical systems.

Time-of-arrival–based localization algorithm in mixed line-of-sight/non-line-of-sight environments

A novel time-of-arrival–based localization algorithm in mixed line-of-sight/non-line-of-sight environments is proposed. First, an optimization problem of target localization in the known distribution of line-of-sight and non-line-of-sight is established, and mixed semi-definite and second-order cone programming techniques are used to transform the original problem into a convex optimization problem which can be solved efficiently. Second, a worst-case robust least squares criterion is used to form an optimization problem of target localization in unknown distribution of line-of-sight and non-line-of-sight, where all links are treated as non-line-of-sight links. This problem is also solved using the similar techniques used in the known distribution of line-of-sight and non-line-of-sight case. Finally, computer simulation results show that the proposed algorithms have better performance in both the known distribution and the unknown distribution of line-of-sight and non-line-of-sight environments.

Additive slacks-based measure: Computational strategy and extension to network DEA

The current paper visits a set of data envelopment analysis (DEA) models that identify inefficiency by optimizing input and output slacks. These slacks are aggregated either in an additive or ratio form. Only the ratio slacks-based DEA models can be solved as a linear program and generate a DEA score between zero and unity. The additive slacks-based model can be equivalent to the Russell graph measure and converted into a second order cone programming (SOCP) problem whose solving procedure has become a mature technology. As such, the additive slacks-based model can also yield a DEA score between zero and unity. This study shows that the additive slacks-based model can be applied to modelling network DEA where the internal structures of decision making units (DMUs) are of interest. The additive slacks-based network DEA can be solved using SOCP technique and adapted to the preference of the decision maker by choosing the weights for aggregating individual components in the network structures. It is shown that the additive slacks-based approach can yield divisional efficiencies of Pareto optimal equivalences to be selected by the decision maker when compared to the existing ratio slacks-based measure. An example and solving codes are provided in the current study.

Scalable enumeration approach for maximizing hosting capacity of distributed generation

At the stage of planning distributed generation (DG) for a distribution network, the network configuration is a key factor in increasing the DG hosting capacity. The determination of a configuration that maximizes the hosting capacity is a highly complex, nonlinear combinatorial optimization problem. No existing method can yield the global optimal solution for practical-scale networks. Therefore, this paper proposes a scalable optimization method. Specifically, the proposed method enumerates all optimal configurations while simultaneously considering optimal DG placement. The proposed method first optimizes the DG placement for possible partial networks using a second-order cone programming technique. Next, it enumerates possible combinations of the partial networks while avoiding a combinatorial explosion using a highly compressed data structure. Finally, it finds the optimal configurations by exploring solutions over the data structure. In experiments involving a large-scale network containing 235 switches, our enumeration method obtained 1.49×1018 global optimal configurations in 17.1 h. Another powerful feature of our method is that it enables distribution system operators to select the preferred optimal configuration interactively.

Robust Thevenin Equivalent Parameter Estimation for Voltage Stability Assessment

This letter presents a robust approach to accurate estimation of Thevenin equivalent (TE) parameters using phasor measurement unit (PMU) data for online voltage stability assessment. The TE parameter estimation is formulated as a worst-case robust least squares problem to take PMU uncertainties into account. A second-order cone programming technique is then utilized to solve the problem. Case studies on several IEEE standard networks and a practical power system, along with comparative results, illustrate the effectiveness and robustness of the presented approach.

Yield surface approximation for lower and upper bound yield design of 3D composite frame structures

The present contribution advocates an up-scaling procedure for computing the limit loads of spatial structures made of composite beams. The resolution of an auxiliary yield design problem leads to the determination of a yield surface in the space of axial force and bending moments. A general method for approximating the numerically computed yield surface by a sum of several ellipsoids is developed. The so-obtained analytical expression of the criterion is then incorporated in the yield design calculations of the whole structure, using second-order cone programming techniques. An illustrative application to a complex spatial frame structure is presented.

Application of discontinuity layout optimization to three-dimensional plasticity problems

A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

Convex Optimization Strategies for Coordinating Large-Scale Robot Formations

This paper investigates convex optimization strategies for coordinating a large-scale team of fully actuated mobile robots. Our primary motivation is both algorithm scalability as well as real-time performance. To accomplish this, we employ a formal definition from shape analysis for formation representation and repose the motion planning problem to one of changing (or maintaining) the shape of the formation. We then show that optimal solutions, minimizing either the total distance or minimax distance the nodes must travel, can be achieved through second-order cone programming techniques. We further prove a theoretical complexity for the shape problem of O(m1.5) as well as O(m) complexity in practice, where m denotes the number of robots in the shape configuration. Solutions for large-scale teams (1000's of robots) can be calculated in real time on a standard desktop PC. Extensions integrating both workspace and vehicle motion constraints are also presented with similar complexity bounds. We expect these results can be generalized for additional motion planning tasks, and will prove useful for improving the performance and extending the mission lives of large-scale robot formations as well as mobile ad hoc networks.

An introduction to convex optimization for communications and signal processing

Convex optimization methods are widely used in the design and analysis of communication systems and signal processing algorithms. This tutorial surveys some of recent progress in this area. The tutorial contains two parts. The first part gives a survey of basic concepts and main techniques in convex optimization. Special emphasis is placed on a class of conic optimization problems, including second-order cone programming and semidefinite programming. The second half of the survey gives several examples of the application of conic programming to communication problems. We give an interpretation of Lagrangian duality in a multiuser multi-antenna communication problem; we illustrate the role of semidefinite relaxation in multiuser detection problems; we review methods to formulate robust optimization problems via second-order cone programming techniques