Formulation Of Constrained Optimization Problem Research Articles

Physics and equality constrained artificial neural networks: Application to forward and inverse problems with multi-fidelity data fusion

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective function as soft penalties. Here, we show that this specific way of formulating the objective function is the source of severe limitations in the PINN approach when applied to different kinds of PDEs. To address these limitations, we propose a versatile framework based on a constrained optimization problem formulation, where we use the augmented Lagrangian method (ALM) to constrain the solution of a PDE with its boundary conditions and any high-fidelity data that may be available. Our approach is adept at forward and inverse problems with multi-fidelity data fusion. We demonstrate the efficacy and versatility of our physics- and equality-constrained deep-learning framework by applying it to several forward and inverse problems involving multi-dimensional PDEs. Our framework achieves orders of magnitude improvements in accuracy levels in comparison with state-of-the-art physics-informed neural networks.

Synchronous Optimal Modulation: Frequency or Time Domain, Global or Constrained Optimization? 40 Years to the First Formulation

Alternative approaches to total harmonic distortion (THD) minimization comprise frequency or time domain THD calculations and global or constrained optimization problem formulation. Time domain constrained optimization formulation suggested in 1977 that seems most adequate from computational efficiency and robustness does not attract sufficient attention it deserves from the modern researchers. Time domain current THD/harmonic loss constrained optimization is illustrated by single-phase inverter examples. New results on multilevel THD optimization for variable voltage levels are presented.

Fuzzy Based Multi-Objective Evolutionary Algorithm for Optimal Location of FACTS Devices in a Power System

This paper presents a Multi Objective Evolutionary Algorithm (MOEA) to solve nonlinear power system optimization problem. The optimization is done with three variables; choice, location and rating of FACTS devices. The targeted technical objectives are; to control the power flow, increase the transmission line capability to its maximum thermal limits, to keep the voltages within limits while minimizing losses. The parameters of objectives are optimized independently and then the formulation of a nonlinear constrained multi-objective optimization problem is done while carrying out concurrent optimization taking two and three objectives. A Fuzzy min max approach is incorporated to reduce the best solution out of non dominated Pareto optimal set. Assessments have been done on IEEE 14 and IEEE 30 bus system for different loading conditions with two devices SVC and TCSC modeled in steady state and the results affirm the potency of the propound approach.

Controlled-distortion constrained global parametrization

The quality of a global parametrization is determined by a number of factors, including amount of distortion, number of singularities (cones), and alignment with features and boundaries. Placement of cones plays a decisive role in determining the overall distortion of the parametrization; at the same time, feature and boundary alignment also affect the cone placement. A number of methods were proposed for automatic choice of cone positions, either based on singularities of cross-fields and emphasizing alignment, or based on distortion optimization. In this paper we describe a method for placing cones for seamless global parametrizations with alignment constraints. We use a close relation between variation-minimizing cross-fields and related 1-forms and conformal maps, and demonstrate how it leads to a constrained optimization problem formulation. We show for boundary-aligned parametrizations metric distortion may be reduced by cone chains , sometimes to an arbitrarily small value, and the trade-off between the distortion and the number of cones can be controlled by a regularization term. Constrained parametrizations computed using our method have significantly lower distortion compared to the state-of-the art field-based method, yet maintain feature and boundary alignment. In the most extreme cases, parametrization collapse due to alignment constraints is eliminated.

Linear Precoding for MIMO Broadcast Channels With Finite-Alphabet Constraints

We investigate the design of linear transmit precoder for multiple-input multiple-output (MIMO) broadcast channels (BC) with finite alphabet input signals. We first derive an explicit expression for the achievable rate region of the MIMO BC with discrete constellation inputs, which is generally applicable to cases involving arbitrary user number and arbitrary antenna number. We further present a weighted sum rate upper bound of the MIMO BC with identical transmit precoding matrices. The resulting bound exhibits a serious performance loss because of the non-uniquely decodable transmit signals for MIMO BC with finite alphabet inputs in high signal-to-noise ratio (SNR) region. This performance loss motivates the use of a simple precoding to combat the non-unique decodability. Based on a constrained optimization problem formulation, we apply the Karush-Kuhn-Tucker analysis to derive necessary conditions for MIMO BC precoders to maximize the weighted sum-rate. We then propose an iterative gradient descent algorithm with backtracking line search to optimize the linear precoders for each user. Our { simulation} results under the practical transmit symbols of discrete constellations demonstrate significant gains by the proposed algorithm over other precoding schemes including the traditional iterative water-filling (WF) design for the Gaussian input signals. For the low-density parity-check coded systems, our precoder provides considerably coded BER improvement through iterative decoding and detection.

Cross-Layer Resource Allocation Scheme Under Heterogeneous Constraints for Next Generation High Rate WPAN

In the next generation wireless networks, the growing demand for new wireless applications is accompanied with high expectations for better quality of service (QoS) fulfillment especially for multimedia applications. Furthermore, the coexistence of future unlicensed users with existing licensed users is becoming a challenging task in the next generation communication systems to overcome the underutilization of the spectrum. A QoS and interference aware resource allocation is thus of special interest in order to respond to the heterogeneous constraints of the next generation networks. In this work, we address the issue of resource allocation under heterogeneous constraints for unlicensed multiband ultra-wideband (UWB) systems in the context of Future Home Networks, i.e. the wireless personal area network (WPAN). The problem is first studied analytically using a heterogeneous constrained optimization problem formulation. After studying the characteristics of the optimal solution, we propose a low-complexity suboptimal algorithm based on a cross-layer approach that combines information provided by the PHY and MAC layers. While the PHY layer is responsible for providing the channel quality of the unlicensed UWB users as well as their interference power that they cause on licensed users, the MAC layer is responsible for classifying the unlicensed users using a two-class based approach that guarantees for multimedia services a high-priority level compared to other services. Combined in an efficient and simple way, the PHY and MAC information present the key elements of the aimed resource allocation. Simulation results demonstrate that the proposed scheme provides a good tradeoff between the QoS satisfaction of the unlicensed applications with hard QoS requirements and the limitation of the interference affecting the licensed users.

DS-CDMA chip waveform design for minimal interference under bandwidth, phase, and envelope constraints

This paper investigates the effect of chip waveform shaping on the error performance, bandwidth confinement, phase continuity, and envelope uniformity in direct-sequence code-division multiple-access communication systems employing offset quadrature modulation formats. An optimal design methodology is developed for the problem of minimizing the multiple-access interference power under various desirable signal constraints, including limited 99% and 99.9% power bandwidth occupancies, continuous signal phase, and near-constant envelope. The methodology is based on the use of prolate spheroidal wave functions to obtain a reduced-dimension discrete constrained optimization problem formulation. Numerous design examples are discussed to compare the performance achieved by the optimally-designed chip waveforms with other conventional schemes, such as offset quadrature phase-shift keying, minimum-shift keying (MSK), sinusoidal frequency-shift keying (SFSK), and time-domain raised-cosine pulses. In general, it is found that while the optimized chip pulses achieved substantial gains when no envelope constraints were imposed, these gains vanish when a low envelope fluctuation constraint was introduced. In particular, it is also shown that MSK is quasi-optimal with regard to the 99% bandwidth measure, while the raised-cosine pulse is equally good with both the 99% and 99.9% measures, but at the expense of some envelope variation. On the other hand, SFSK is quasi-optimal with regard to the 99.9% bandwidth occupancy, among the class of constant-to-low envelope variation pulses.