40 research outputs found
MM Algorithms for Geometric and Signomial Programming
This paper derives new algorithms for signomial programming, a generalization
of geometric programming. The algorithms are based on a generic principle for
optimization called the MM algorithm. In this setting, one can apply the
geometric-arithmetic mean inequality and a supporting hyperplane inequality to
create a surrogate function with parameters separated. Thus, unconstrained
signomial programming reduces to a sequence of one-dimensional minimization
problems. Simple examples demonstrate that the MM algorithm derived can
converge to a boundary point or to one point of a continuum of minimum points.
Conditions under which the minimum point is unique or occurs in the interior of
parameter space are proved for geometric programming. Convergence to an
interior point occurs at a linear rate. Finally, the MM framework easily
accommodates equality and inequality constraints of signomial type. For the
most important special case, constrained quadratic programming, the MM
algorithm involves very simple updates.Comment: 16 pages, 1 figur
A Block Minorization--Maximization Algorithm for Heteroscedastic Regression
The computation of the maximum likelihood (ML) estimator for heteroscedastic
regression models is considered. The traditional Newton algorithms for the
problem require matrix multiplications and inversions, which are bottlenecks in
modern Big Data contexts. A new Big Data-appropriate minorization--maximization
(MM) algorithm is considered for the computation of the ML estimator. The MM
algorithm is proved to generate monotonically increasing sequences of
likelihood values and to be convergent to a stationary point of the
log-likelihood function. A distributed and parallel implementation of the MM
algorithm is presented and the MM algorithm is shown to have differing time
complexity to the Newton algorithm. Simulation studies demonstrate that the MM
algorithm improves upon the computation time of the Newton algorithm in some
practical scenarios where the number of observations is large
Joint Pilot Design and Uplink Power Allocation in Multi-Cell Massive MIMO Systems
This paper considers pilot design to mitigate pilot contamination and provide
good service for everyone in multi-cell Massive multiple input multiple output
(MIMO) systems. Instead of modeling the pilot design as a combinatorial
assignment problem, as in prior works, we express the pilot signals using a
pilot basis and treat the associated power coefficients as continuous
optimization variables. We compute a lower bound on the uplink capacity for
Rayleigh fading channels with maximum ratio detection that applies with
arbitrary pilot signals. We further formulate the max-min fairness problem
under power budget constraints, with the pilot signals and data powers as
optimization variables. Because this optimization problem is non-deterministic
polynomial-time hard due to signomial constraints, we then propose an algorithm
to obtain a local optimum with polynomial complexity. Our framework serves as a
benchmark for pilot design in scenarios with either ideal or non-ideal
hardware. Numerical results manifest that the proposed optimization algorithms
are close to the optimal solution obtained by exhaustive search for different
pilot assignments and the new pilot structure and optimization bring large
gains over the state-of-the-art suboptimal pilot design.Comment: 16 pages, 8 figures. Accepted to publish at IEEE Transactions on
Wireless Communication
Optimization techniques applied to passive measures for in-orbit spacecraft survivability
Spacecraft designers have always been concerned about the effects of meteoroid impacts on mission safety. The engineering solution to this problem has generally been to erect a bumper or shield placed outboard from the spacecraft wall to disrupt/deflect the incoming projectiles. Spacecraft designers have a number of tools at their disposal to aid in the design process. These include hypervelocity impact testing, analytic impact predictors, and hydrodynamic codes. Analytic impact predictors generally provide the best quick-look estimate of design tradeoffs. The most complete way to determine the characteristics of an analytic impact predictor is through optimization of the protective structures design problem formulated with the predictor of interest. Space Station Freedom protective structures design insight is provided through the coupling of design/material requirements, hypervelocity impact phenomenology, meteoroid and space debris environment sensitivities, optimization techniques and operations research strategies, and mission scenarios. Major results are presented
Global optimisation for a developed price discrimination model:A signomial geometric programming-based approach
This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer objective is to maximize the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set up costs and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions
Optimization-based design of fault-tolerant avionics
This dissertation considers the problem of improving the self-consciousness for avionic systems using numerical optimization techniques, emphasizing UAV applications. This self-consciousness implies a sense of awareness for oneself to make a reliable decision on some crucial aspects. In the context of the avionics or aerospace industry, those aspects are SWaP-C as well as safety and reliability. The decision-making processes to optimize these aspects, which are the main contributions of this work, are presented. In addition, implementation on various types of applications related to avionics and UAV are also provided.
The first half of this thesis lays out the background of avionics development ranging from a mechanical gyroscope to a current state-of-the-art electronics system. The relevant mathematics regarding convex optimization and its algorithms, which will be used for formulating this self-consciousness problem, are also provided.
The latter half presents two problem formulations for redundancy design automation and reconfigurable middleware. The first formulation focuses on the minimization of SWaP-C while satisfying safety and reliability requirements. The other one aims to maximize the system safety and reliability by introducing a fault-tolerant capability via the task scheduler of middleware or RTOS. The usage of these two formulations is shown by four aerospace applications---reconfigurable multicore avionics, a SITL simulation of a UAV GNC system, a modular drone, and a HITL simulation of a fault-tolerant distributed engine control architecture.Ph.D
Global optimisation for a developed price discrimination model:A signomial geometric programming-based approach
This paper presents a price discrimination model for a manufacturer who acts in two different markets. In order to have a fair price discrimination model and compare monopoly and competitive markets, it is assumed that there is no competitor in the first market (monopoly market) and there is a strong competitor in the other market (competitive market). The manufacturer objective is to maximize the total benefit in both markets. The decision variables are selling price, lot size, marketing expenditure, customer service cost, flexibility and reliability of production process, set up costs and quality of products. The proposed model in this paper is a signomial geometric programming problem which is difficult to solve and find the globally optimal solution. So, this signomial model is converted to a posynomial geometric type and using an iterative method, the globally optimal solution is found. To illustrate the capability of the proposed model, a numerical example is solved and the sensitivity analysis is implemented under different conditions