Initial Feasible Point Research Articles

A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

AbstractThis article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.

Application of Numerical Nonlinear Optimization Problems

Abstract: In this paper develops a method based on fuzzy logic for solving linear approximation relationship nonlinear optimization problems. In the proposed method, the nonlinear objective function as well as the constrained functions forming the feasible regions is linearly approximated about an initial feasible point by Taylors Series and then the nonlinear optimization problem is approximated to a linear optimization problem or a linear programming problem. The concept of fuzzy decision making is iteratively applied to find the fuzzy optimal solution of the problem.

RSS-Based Multiple Co-Channel Sources Localization With Unknown Shadow Fading and Transmitted Power

Multi-source localization based on received signal strength has drawn great interest in wireless sensor networks. However, the shadow fading term caused by obstacles cannot be separated from the received signal, which leads to severe error in location estimate. In this paper, we approximate the log-normal sum distribution through Fenton-Wilkinson method to formulate a non-convex maximum likelihood (ML) estimator with unknown shadow fading factor and transmitted power. In order to overcome the difficulty in solving the non-convex problem, we propose a novel algorithm to estimate the locations of sources. Specifically, the region is divided into <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$N$</tex-math></inline-formula> grids firstly, and the multi-source localization is converted into a sparse recovery problem so that we can obtain the sparse solution. Then we utilize the k-means clustering method to obtain the rough locations of the off-grid sources as the initial feasible point of the ML estimator. Finally, an iterative refinement of the estimated locations is proposed by dynamic updating of the localization dictionary. The proposed algorithm can efficiently approach a superior local optimal solution of the ML estimator. It is shown from the simulation results that the proposed method has a promising localization performance and improves the robustness for co-channel multi-source localization in shadow fading environments. Moreover, the proposed method provides a better computational complexity from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(K^{3}\,N^{3})$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$O(N^{3})$</tex-math></inline-formula> .

Cooperative Beamforming for Wireless Fronthaul and Access Links in Ultra-Dense C-RANs With SWIPT: A First-Order Approach

This work studies multigroup multicasting transmission in cloud radio access networks (C-RANs) with simultaneous wireless information and power transfer, where densely packed remote radio heads (RRHs) cooperatively provide information and energy services for information users (IUs) and energy users (EUs), respectively. To maximize the weighted sum rate (WSR) of information services while satisfying the energy harvesting levels at EUs, an optimization of joint beamforming design for the fronthaul and access links is formulated, which is however neither smooth nor convex and is indeed NP-hard. To tackle this difficulty, the smooth and successive convex approximations are used to transform the original problem into a sequence of convex problems, and two first-order algorithms are developed to find the initial feasible point and the nearly optimal solution, respectively. Moreover, an accelerated algorithm is designed to improve the convergence speed by exploiting both Nesterov and heavy-ball momentums. Numerical results demonstrate that the proposed first-order algorithms achieve almost the same WSR as that of traditional second-order approaches yet with much lower computational complexity, and the proposed scheme outperforms state-of-the-art competing schemes in terms of WSR.

Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance

Γ-maximin, Γ-maximax and interval dominance are familiar decision criteria for making decisions under severe uncertainty, when probability distributions can only be partially identified. One can apply these three criteria by solving sequences of linear programs. In this study, we present new algorithms for these criteria and compare their performance to existing standard algorithms. Specifically, we use efficient ways, based on previous work, to find common initial feasible points for these algorithms. Exploiting these initial feasible points, we develop early stopping criteria to determine whether gambles are either Γ-maximin, Γ-maximax or interval dominant. We observe that the primal-dual interior point method benefits considerably from these improvements. In our simulation, we find that our proposed algorithms outperform the standard algorithms when the size of the domain of lower previsions is less or equal to the sizes of decisions and outcomes. However, our proposed algorithms do not outperform the standard algorithms in the case that the size of the domain of lower previsions is much larger than the sizes of decisions and outcomes.

An Efficient Batch-Constrained Bayesian Optimization Approach for Analog Circuit Synthesis via Multiobjective Acquisition Ensemble

Bayesian optimization is a promising methodology for analog circuit synthesis. However, the sequential nature of the Bayesian optimization framework significantly limits its ability to fully utilize real-world computational resources. In this paper, we propose an efficient parallelizable Bayesian optimization algorithm via Multi-objective ACquisition function Ensemble (MACE) to further accelerate the optimization procedure. By sampling query points from the Pareto front of the probability of improvement (PI), expected improvement (EI) and lower confidence bound (LCB), we combine the benefits of state-of-the-art acquisition functions to achieve a delicate tradeoff between exploration and exploitation for the unconstrained optimization problem. Based on this batch design, we further adjust the algorithm for the constrained optimization problem. By dividing the optimization procedure into two stages and first focusing on finding an initial feasible point, we manage to gain more information about the valid region and can better avoid sampling around the infeasible area. After achieving the first feasible point, we favor the feasible region by adopting a specially designed penalization term to the acquisition function ensemble. The experimental results quantitatively demonstrate that our proposed algorithm can reduce the overall simulation time by up to 74 times compared to differential evolution (DE) for the unconstrained optimization problem when the batch size is 15. For the constrained optimization problem, our proposed algorithm can speed up the optimization process by up to 15 times compared to the weighted expected improvement based Bayesian optimization (WEIBO) approach, when the batch size is 15.

Energy-Efficient Non-Orthogonal Multicast and Unicast Transmission of Cell-Free Massive MIMO Systems With SWIPT

This work investigates the energy-efficient resource allocation for layered-division multiplexing (LDM) based non-orthogonal multicast and unicast transmission in cell-free massive multiple-input multiple-output (MIMO) systems, where each user equipment (UE) performs wireless information and power transfer simultaneously. To begin with, the achievable data rates for multicast and unicast services are derived in closed form, as well as the received radio frequency (RF) power at each UE. Based on the analytical results, a nonsmooth and nonconvex optimization problem for energy efficiency (EE) maximization is formulated, which is however a challenging fractional programming problem with complex constraints. To suit the massive access setting, a first-order algorithm is developed to find both initial feasible point and the nearly optimal solution. Moreover, an accelerated algorithm is designed to improve the convergence speed. Numerical results demonstrate that the proposed first-order algorithms can achieve almost the same EE as that of second-order approaches yet with much lower computational complexity, which provides insight into the superiority of the proposed algorithms for massive access in cell-free massive MIMO systems.

Feasible Path Identification in Optimal Power Flow With Sequential Convex Restriction

Nonconvexity induced by the nonlinear AC power flow equations challenges solution algorithms for AC optimal power flow (OPF) problems. While significant research efforts have focused on reliably computing high-quality OPF solutions, it is not always clear that there exists a feasible path to reach the desired operating point. Transitioning between operating points while avoiding constraint violations can be challenging since the feasible space of the OPF problem is nonconvex and potentially disconnected. To address this problem, we propose an algorithm that computes a provably feasible path from an initial operating point to a desired operating point. Given an initial feasible point, the algorithm solves a sequence of convex quadratically constrained optimization problems over conservative convex inner approximations of the OPF feasible space. In each iteration, we obtain a new, improved operating point and a feasible transition from the operating point in the previous iteration. In addition to computing a feasible path to a known desired operating point, this algorithm can also be used to improve the operating point locally. Extensive numerical studies on a variety of test cases demonstrate the algorithm and the ability to arrive at a high-quality solution in few iterations.

Primal-Dual Interior-Point Technique for Optimisation of 330kV Power System on One Variable

The work deal on a method for optimisation of 330KV power system load flow which excels other existing methods.This method is called, PRIMAL-DUAL INTERIOR-POINT TECHNIQUE for solving optimal load flow problem. As problems of load-shedding, power outages and system losses have been cause for worries, especially among the developing nations such as Nigeria, hence need for a load flow solution technique, which, this work addresses. Optimisation is achieving maximum of required and minimum of un-required and it is obtained mathematically by differentiating the objective function with respect to the control variable(s) and equating the resulting expression(s) to zero. In 330KV Power System, optimization is maximisation of real power injection, voltage magnitude and cost effectiveness, while minimization of reactive power injection, power loss, critical clearing time of fault conditions and time of load flow simulation.. This work developed a mathematical model that solves load flow problems by engaging non-negative PRIMAL variables, “S” and “z” into the inequality constraint of the load flow problems in other to transform it to equality constraint(s). Another non-negative DUAL variables “” and “v” are incorporated together with Lagrangian multiplier “?” to solve optimisation. While solving optimisation Barrier Parameter “” which ensures feasible point(s) exist(s) within the feasible region (INTERIOR POINT). Damping factor or step length parameter “?”, in conjunction with Safety factor “” (which improves convergence and keeps the non-negative variables strictly positive) are employed to achieve result. The key-words which are capitalized joined to give this work its name, the PRIMAL-DUAL INTERIOR-POINT. The initial feasible point(s) is/are tested for convergence and where it/they fail(s), iteration starts. Variables are updated by using the computed step size and the step length parameter “?”, which thereafter, undergo another convergence test. This technique usually converges after first iteration. Primarily, this technique excels the existing methods as; it solves load flow problems with equality and inequality constraints simultaneously, it often converges after first iteration as against six or more iterations of the existing methods, its solution provides higher power generations from available capacity and minimum system loss. Example, Geregu Power Station on Bus 12 generates 0.1786p.u power from the available 0.2000p.u through the PD-IP tech. as against 0.1200p.u of the existing methods. Also it supplies 0.1750p.u with loss of 0.0036p.u as against 0.0236p.u with loss of 0.0964p.u of the existing methods. This results in 90% generation as against 60% of existing methods. Generation loss is 1.8% as against 80.3% of existing methods and availability loss of 12.5% as against 88.2% of existing. Therefore this method ensures very high system stability.

Primal-Dual Interior-Point Technique for Optimisation of 330kV Power System on One Variable

The work deal on a method for optimisation of 330KV power system load flow which excels other existing methods.This method is called, PRIMAL-DUAL INTERIOR-POINT TECHNIQUE for solving optimal load flow problem. As problems of load-shedding, power outages and system losses have been cause for worries, especially among the developing nations such as Nigeria, hence need for a load flow solution technique, which, this work addresses. Optimisation is achieving maximum of required and minimum of un-required and it is obtained mathematically by differentiating the objective function with respect to the control variable(s) and equating the resulting expression(s) to zero. In 330KV Power System, optimization is maximisation of real power injection, voltage magnitude and cost effectiveness, while minimization of reactive power injection, power loss, critical clearing time of fault conditions and time of load flow simulation.. This work developed a mathematical model that solves load flow problems by engaging non-negative PRIMAL variables, “S” and “z” into the inequality constraint of the load flow problems in other to transform it to equality constraint(s). Another non-negative DUAL variables “” and “v” are incorporated together with Lagrangian multiplier “λ” to solve optimisation. While solving optimisation Barrier Parameter “” which ensures feasible point(s) exist(s) within the feasible region (INTERIOR POINT). Damping factor or step length parameter “α”, in conjunction with Safety factor “” (which improves convergence and keeps the non-negative variables strictly positive) are employed to achieve result. The key-words which are capitalized joined to give this work its name, the PRIMAL-DUAL INTERIOR-POINT. The initial feasible point(s) is/are tested for convergence and where it/they fail(s), iteration starts. Variables are updated by using the computed step size and the step length parameter “α”, which thereafter, undergo another convergence test. This technique usually converges after first iteration. Primarily, this technique excels the existing methods as; it solves load flow problems with equality and inequality constraints simultaneously, it often converges after first iteration as against six or more iterations of the existing methods, its solution provides higher power generations from available capacity and minimum system loss. Example, Geregu Power Station on Bus 12 generates 0.1786p.u power from the available 0.2000p.u through the PD-IP tech. as against 0.1200p.u of the existing methods. Also it supplies 0.1750p.u with loss of 0.0036p.u as against 0.0236p.u with loss of 0.0964p.u of the existing methods. This results in 90% generation as against 60% of existing methods. Generation loss is 1.8% as against 80.3% of existing methods and availability loss of 12.5% as against 88.2% of existing. Therefore this method ensures very high system stability.

NOMA-Enabled Layered Video Multicast in Wireless-Powered Relay Systems

This letter proposes a novel layered video multicast scheme for wireless-powered relay systems, where the multi-antenna base station multicasts layered video signals over non-orthogonal multiple access (NOMA) to heterogeneous user groups with the help of a dedicated relay. To minimize the average transmission power of the base station, an optimization problem is formulated to jointly design the energy signal power and layered video multicast beamformers, while guaranteeing all the users’ quality of experience (QoE), i.e., fluent video playback and successful decoding of video signals. Since the formulated optimization problem is non-convex, a low-complexity algorithm is developed to obtain a local minimum, and a novel initial feasible point search algorithm is proposed to initialize the solving process. Simulation results reveal that the proposed scheme works well and can greatly reduce the power consumption.

A Framework for Weighted-Sum Energy Efficiency Maximization in Wireless Networks

Weighted-sum energy efficiency (WSEE) is a key performance metric in heterogeneous networks, where the nodes may have different energy efficiency (EE) requirements. Nevertheless, WSEE maximization is a challenging problem due to its nonconvex sum-of-ratios form. Unlike previous work, this paper presents a systematic approach to WSEE maximization under not only power constraints, but also data rate constraints, using a general SINR expression. In particular, the original problem is transformed into an equivalent form, and then a sequential convex optimization (SCO) algorithm is proposed. This algorithm is theoretically guaranteed to converge for any initial feasible point, and, under suitable constraint qualifications, achieves a Karush-Kuhn-Tucker (KKT) solution. Furthermore, we provide remarkable extensions to the proposed methodology, including systems with multiple resource blocks as well as a more general power consumption model which is not necessarily a convex function of the transmit powers. Finally, numerical analysis reveals that the proposed algorithm exhibits fast convergence, low complexity, and robustness (insensitivity to initial points).

An Algorithm for Solving Indefinite Quadratic Programming Problems

In this paper, we give in section (1) compact description of the algorithm for solving general quadratic programming problems (that is, obtaining a local minimum of a quadratic function subject to inequality constraints) is presented. In section (2), we give practical application of the algorithm, we also discuss the computation work and performing by the algorithm and try to achieve efficiency and stability as possible as we can. In section (3), we show how to update the QR-factors of , when the tableau is complementary ,we give updating to the LDLT-Factors of . In section (4) we are not going to describe a fully detailed method of obtaining an initial feasible point, since linear programming literature is full of such techniques.

Iterative Convex Overbounding Algorithms for BMI Optimization Problems

This paper considers Iterative Convex Overbounding (ICO) techniques for Bilinear Matrix Inequality (BMI) problems. It is very common for BMIs to be present in multi-objective control, as well as many other optimization problems. Theoretically, ICO techniques guarantee monotonic convergence to a local optimum, and do not require the introduction of conservatism or relaxations. In this work, we propose an update to ICO which allows for improved results and a new convergence path. We also illustrate that ICO techniques are extensible to problems in which initial feasible design points are not known. Finally, we illustrate that ICO can be extended to matrix polynomial inequalities of arbitrary finite order. These ideas are demonstrated on a simple example.

Automated Method for Optimizing Feasible Locations of Mobile Cranes Based on 3D Visualization

The precise operation of mobile cranes contributes to the safety and efficiency of lift works, among which accurate location is one of the most critical aspects. Considering the complexities and dynamics of construction sites, this paper presents an approach for crane location determination based on the simulation of mobile crane operations. First a data processing method is developed to enable the automated conversion from BIM (Building Information Modeling) and schedule plan to the simulation system. Then the reachability and work radius of mobile cranes are examined for selecting the initial feasible location points. The bounding box method is used for the collision detection to ensure the safety of crane operations. Also, the minimum number of relocation and the lift time are taken into account to determine the final feasible location points of mobile cranes.

A feasible direction algorithm for general nonlinear semidefinite programming

This paper deals with nonlinear smooth optimization problems with equality and inequality constraints, as well as semidefinite constraints on nonlinear symmetric matrix-valued functions. A new semidefinite programming algorithm that takes advantage of the structure of the matrix constraints is presented. This one is relevant in applications where the matrices have a favorable structure, as in the case when finite element models are employed. FDIPA_GSDP is then obtained by integration of this new method with the well known Feasible Direction Interior Point Algorithm for nonlinear smooth optimization, FDIPA. FDIPA_GSDP makes iterations in the primal and dual variables to solve the first order optimality conditions. Given an initial feasible point with respect to the inequality constraints, FDIPA_GSDP generates a feasible descent sequence, converging to a local solution of the problem. At each iteration a feasible descent direction is computed by merely solving two linear systems with the same matrix. A line search along this direction looks for a new feasible point with a lower objective. Global convergence to stationary points is proved. Some structural optimization test problems were solved very efficiently, without need of parameters tuning.

Primal and dual active-set methods for convex quadratic programming

Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables. In the first part of the paper, two methods are proposed, one primal and one dual. These methods generate a sequence of iterates that are feasible with respect to the equality constraints associated with the optimality conditions of the primal-dual form. The primal method maintains feasibility of the primal inequalities while driving the infeasibilities of the dual inequalities to zero. The dual method maintains feasibility of the dual inequalities while moving to satisfy the primal inequalities. In each of these methods, the search directions satisfy a KKT system of equations formed from Hessian and constraint components associated with an appropriate column basis. The composition of the basis is specified by an active-set strategy that guarantees the nonsingularity of each set of KKT equations. Each of the proposed methods is a conventional active-set method in the sense that an initial primal- or dual-feasible point is required. In the second part of the paper, it is shown how the quadratic program may be solved as a coupled pair of primal and dual quadratic programs created from the original by simultaneously shifting the simple-bound constraints and adding a penalty term to the objective function. Any conventional column basis may be made optimal for such a primal-dual pair of shifted-penalized problems. The shifts are then updated using the solution of either the primal or the dual shifted problem. An obvious application of this approach is to solve a shifted dual QP to define an initial feasible point for the primal (or vice versa). The computational performance of each of the proposed methods is evaluated on a set of convex problems.

On the Solution of a Nonlinear Semidefinite Program Arising in Discrete-Time Feedback Control Design

A sequential quadratic programming method with line search is analyzed and studied for finding the local solution of a nonlinear semidefinite programming problem resulting from the discrete-time output feedback problem. The method requires an initial feasible point with respect to two positive definite constraints. By parameterizing the optimization problem we ease that requirement. The method is tested numerically on several test problems chosen from the benchmark collection (Leibfritz, 2004).

A Weighted Target- following Algorithm for Linearly Constrained Convex Optimization

In recent years, convex optimization solved very large practical engineering problems reliably and eciently. In this paper, we present an extension of an algorithm for convex quadratic programming using a new technique for nding a class of search directions and the strategy of the central path, for convex optimization under linear constraints. To solve the initialization problem, we have introduced a weighted vector with the property that starting from an initial feasible centred point, it generates iterates that simultaneously, gets closer to optimality and closer to centrality. Finally, the favorable polynomial complexity bound for the algorithm is deserved namely, O ( p n log( x t z )) iterations.

Joint Optimization of Source Power Allocation and Distributed Relay Beamforming in Multiuser Peer-to-Peer Relay Networks

In this paper, we consider the joint optimization of the source power allocation and relay beamforming weights in distributed multiuser peer-to-peer (MUP2P) relay networks applying the amplify-and-forward (AF) protocol. We adopt a quality-of-service (QoS) based approach, in which the total power transmitted from all sources and relays is minimized while guaranteeing the prescribed QoS requirement of each source-destination pair. The QoS is modeled as a function of the receive signal-to-interference-plus-noise ratio (SINR) at the destinations. Unlike the existing contributions, the transmitted powers of the sources and the beamforming weights of the relays are optimized jointly in this paper. Introducing an appropriate transformation of variables, the QoS based source power allocation and distributed relay beamforming (PADB) problem can be equivalently transformed into a difference of convex (DC) program, which can be efficiently solved with local optimality using the constrained concave convex procedure (CCCP). Based on this procedure, we also propose an iterative feasibility search algorithm (IFSA) to find an initial feasible point of the DC program. The analytic study of the proposed solution confirms that it converges to a local optimum of the PADB problem. Numerical results show that our solution outperforms (in terms of the total transmitted power) the alternating optimization procedure and the exact penalty based DC algorithm. In addition, the proposed IFSA outperforms the alternating optimization algorithm in finding feasible points of the DC program (i.e., the equivalence of the PADB problem).