Global minimum point of a convex function

1993 ◽  
Vol 55 (2-3) ◽  
pp. 213-218 ◽  
Author(s):  
J.M. Soriano
Keyword(s):  
Convex Function ◽  
Global Minimum ◽  
Minimum Point ◽  
Global Minimum Point

A singularly perturbed elliptic problem involving supercritical Sobolev exponent

1998 ◽  
Vol 128 (4) ◽  
pp. 809-819 ◽  
Author(s):  
Yaotian Shen ◽  
Shusen Yan
Keyword(s):  
Elliptic Problem ◽  
Local Minimum ◽  
Global Minimum ◽  
Singularly Perturbed ◽  
Minimum Point ◽  
Regular Part ◽  
Local Minimum Point ◽  
Minimisation Problem ◽  
Sobolev Exponent ◽  
Global Minimum Point

This paper deals with −Δu + εuq−1 = u2*−1, , where q > 2*, ε > 0. We first show that the minimiser of the associated minimisation problem blows up at the global minimum point of H(x, x), where H(y, x) is the regular part of the Green's function. We then prove that for each strictly local minimum point x0 of H(x, x), this problem has a solution concentrating at x0 as ε→0.

scholarly journals Roughly geodesic B - r-preinvex functions on Cartan Hadamard manifolds

2018 ◽  
Vol 33 (2) ◽  
pp. 325
Author(s):  
Meraj Ali Khan ◽  
Izhar Ahmad
Keyword(s):  
Optimization Problem ◽  
Global Minimum ◽  
Minimum Point ◽  
Hadamard Manifold ◽  
Hadamard Manifolds ◽  
New Class ◽  
Local Minimum Point ◽  
Preinvex Functions ◽  
Global Minimum Point ◽  
Class Of Functions

In this article, we introduce a new class of functions called roughly geodesic B????r????preinvex on a Hadamard manifold and establish some properties of roughly geodesic B - r-preinvex functions on Hadamard manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under roughly geodesic B-r- preinvexity on Hadamard manifolds. The results presented in this paper extend and generalize the results appeared in the literature.

scholarly journals The Identification of Convex Function on Riemannian Manifold

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Li Zou ◽  
Xin Wen ◽  
Hamid Reza Karimi ◽  
Yan Shi
Keyword(s):  
Riemannian Manifold ◽  
Convex Function ◽  
Global Minimum ◽  
Directional Derivative ◽  
Inequality Constraints ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Generalized Gradient ◽  
Necessary And Sufficient ◽  
Global Minimum Point

The necessary and sufficient condition of convex function is significant in nonlinear convex programming. This paper presents the identification of convex function on Riemannian manifold by use of Penot generalized directional derivative and the Clarke generalized gradient. This paper also presents a method for judging whether a point is the global minimum point in the inequality constraints. Our objective here is to extend the content and proof the necessary and sufficient condition of convex function to Riemannian manifolds.

scholarly journals Generalized Geodesic Convexity on Riemannian Manifolds

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 547 ◽  
Author(s):  
Izhar Ahmad ◽  
Meraj Ali Khan ◽  
Amira A. Ishan
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Global Minimum ◽  
Mean Value ◽  
Mathematical Programming Problem ◽  
Hadamard Manifolds ◽  
Geodesic Convexity ◽  
Invex Functions ◽  
Mean Value Inequality ◽  
Global Minimum Point

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

UAV Formation Control Based on the Improved APF

2014 ◽  
Vol 933 ◽  
pp. 358-364 ◽  
Author(s):  
Jie Yang ◽  
Ke Yi Zhang ◽  
Xin Ming Wang ◽  
Cheng Long Hao ◽  
Tao Wei
Keyword(s):  
Formation Control ◽  
Local Minimum ◽  
Route Planning ◽  
Minimum Point ◽  
Relative Distance ◽  
Random Fluctuation ◽  
Target Point ◽  
Turning Angle ◽  
Fluctuation Method ◽  
Global Minimum Point

Malfunction such as target non-reach ability, local minimum pole and oscillation happens when traditional APF is applied to route planning. This paper proposes an improved APF model, considering the relative distance between the UAV and the target, the relative distance between the lead craft and the wing craft and the safety. We ensure the point of target to be the global minimum point in the entire potential fieldtarget non-reach ability caused by the threat and target point being too close are solved by adopting the modified repulsive potential function; planning failure in which UAVs falling into local minimum point is solved by adopting random fluctuation method; considering the oscillation of traditional potential field, the obstacle link method is proposed. The results of the simulation indicate the single UAV simulation route after obstacles overall planning, track route of UAV formation and formation route with obstacles with turning angle constraints. Requirements of Formation control and formation obstacle avoidance have been well satisfied.

scholarly journals A Global Optimization Algorithm for Unconstrained Non-linear Optimization Problems Using Chaotic Neuron Map and Golden Number

Webology ◽  
2021 ◽  
Vol 18 (Special Issue 05) ◽  
pp. 1118-1136
Author(s):  
G. Sandhya Rani ◽  
Sarada Jayan
Keyword(s):  
Optimization Algorithm ◽  
Global Minimum ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Golden Section ◽  
Linear Optimization ◽  
Second Stage ◽  
Golden Section Search ◽  
Linear Optimization Problems ◽  
Global Minimum Point

This paper presents aninnovative global multi-variable optimization algorithm using one of the best chaotic sequences, the neuron map, a description of which is also provided in the paper. The algorithm uses neuron map in the first stage to move near the global minimum point, as well as in each iteration of the second stage of local search that is done using the N-dimensional golden section search algorithm. The generation and mapping of the neuron variables to the optimization variables along with the stagewise search for the global minimum is explained conscientiously in the work. Numerical results on some benchmark functions and the comparison with a latest state-of-the-art algorithm ispresented in order to demonstrate the efficiency of the proposed algorithm.

Parameter Estimation of a Single Wheel Station using Hybrid Differential Evolution

2003 ◽  
Vol 217 (6) ◽  
pp. 431-447 ◽  
Author(s):  
C Pedchote ◽  
D J Purdy
Keyword(s):  
Parameter Estimation ◽  
Differential Evolution ◽  
Global Minimum ◽  
Estimation Method ◽  
Model Parameters ◽  
Mean Squared Errors ◽  
Gradient Based ◽  
Downhill Simplex ◽  
Global Minimum Point ◽  
Best Fit

This paper investigates an application of a ‘discrete variable’ hybrid differential evolution (dvHDE) method to parameter estimation of a single wheel station. The parameters of the single wheel station represent a quarter of the suspension of a medium sized family car. The estimation method developed incorporated the dvHDE and use of a Kalman filter (KF). The KF provides estimates of the ‘unmeasured’ states of the system being studied. The dvHDE, which works as a function optimizer, provides a ‘best fit’ set of model parameters. The performance of the dvHDE method was examined and compared against the standard gradient-based (GB) method, downhill simplex (DS) method and original differential evolution (DE) method on simulated and experimentally obtained data. The normalized mean squared errors (MSEs) of the system outputs are considered as the fitting criterion in the optimization process. The identified model parameters gave an MSE of below 3.5 per cent. The dvHDE method performed better over the GB, DS and DE methods and has been shown to improve the convergence rate by approximately 19 per cent over the original DE method, without sacrificing ability to find the global minimum point.

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

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