An Improved Direct Search Mathematical Programming Algorithm

1975 ◽  
Vol 97 (4) ◽  
pp. 1305-1310 ◽  
Author(s):  
M. Pappas ◽  
J. Y. Moradi
Keyword(s):  
Mathematical Programming ◽  
Direction Finding ◽  
Direct Search ◽  
Pattern Search ◽  
New Method ◽  
Programming Algorithm ◽  
Test Problems ◽  
Feasible Direction ◽  
Search Termination

An improved, nonlinear, constrained algorithm is presented, coupling a rotating coordinate pattern search with a feasible direction finding procedure used at points of pattern search termination. The procedure is compared with eighteen algorithms, including most of the popular methods, on ten test problems. These problems are such that the majority of codes failed to solve more than half of them. The new method proved superior to all others in the overall generality and efficiency rating, being the only one solving all problems.

Use of Direct Search in Automated Optimal Design

1972 ◽  
Vol 94 (2) ◽  
pp. 395-401 ◽  
Author(s):  
M. Pappas
Keyword(s):  
Optimal Design ◽  
Mathematical Programming ◽  
Penalty Function ◽  
Original Method ◽  
Direct Search ◽  
Search Method ◽  
Pattern Search ◽  
Search Procedure ◽  
Optimal Design Problem ◽  
Variable Step

A direct search penalty function procedure is described for treating a rather general mathematical programming form of the optimal design problem. A rotating coordinate modification of the pattern search of Hooke and Jeeves is proposed and compared with the original method, and an earlier variable step modification, as the basic optimal search method. The algorithm is successfully applied to several design examples which indicate that both modifications are comparable and are significantly superior to the original pattern search procedure.

scholarly journals A Frame-Based Conjugate Gradients Direct Search Method with Radial Basis Function Interpolation Model

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowei Fang ◽  
Qin Ni
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Direct Search ◽  
Search Method ◽  
Conjugate Gradients ◽  
Test Problems ◽  
Interpolation Model ◽  
Direct Search Method ◽  
Radial Basis Function Interpolation ◽  
Radial Basis

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising.

Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

2019 ◽  
Vol 31 (4) ◽  
pp. 689-702 ◽  
Author(s):  
Juliane Müller ◽  
Marcus Day
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Black Box ◽  
Direct Search ◽  
Test Problems ◽  
Large Set ◽  
Mesh Adaptive Direct Search ◽  
Surrogate Optimization ◽  
Computationally Expensive ◽  
Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.

A mathematical programming algorithm for limit analysis

1991 ◽  
Vol 7 (3) ◽  
pp. 267-274 ◽  
Author(s):  
Zhang Pixin ◽  
Lu Mingwan ◽  
Hwang Kehchih
Keyword(s):  
Mathematical Programming ◽  
Limit Analysis ◽  
Programming Algorithm

Frontiers in Engineering Optimization

1983 ◽  
Vol 105 (2) ◽  
pp. 151-154 ◽  
Author(s):  
J. T. Betts
Keyword(s):  
Mathematical Programming ◽  
Engineering Problem ◽  
Theory And Practice ◽  
Programming Algorithm ◽  
Engineering System ◽  
Engineering Optimization ◽  
Complex Engineering ◽  
Optimization Operator

The successful application of a mathematical programming algorithm to a complex engineering problem requires a careful interfacing of needs and requirements between the optimization operator and the engineering system. This paper outlines some areas where interface requirements have not been successfully resolved. In order to bridge the frontier between theory and practice, issues are identified which require resolution by both algorithm developers and system engineers.

A Modification of Feasible Direction Optimization Method for Handling Equality Constraints

1989 ◽  
Vol 111 (3) ◽  
pp. 442-445
Author(s):  
Yong Chen ◽  
Bailin Li
Keyword(s):  
Nonlinear Programming ◽  
Optimization Method ◽  
Direction Finding ◽  
Equality Constraints ◽  
Feasible Region ◽  
Feasible Direction ◽  
Feasible Direction Method ◽  
Traditional Algorithm ◽  
Inequality Type ◽  
Nonlinear Equality

The Feasible Direction Method of Zoutendijk has proven to be one of the most efficient algorithms currently available for solving nonlinear programming problems with only inequality type constraints. Since in the case of equality type constraints, there exists no nonzero direction close to the feasible region, the traditional algorithm cannot work properly. In this paper, a modified feasible direction finding technique has been proposed in order to handle nonlinear equality constraints for the Feasible Direction Method. The algorithm is based on searching along directions intersecting the tangent of the equality constraints at some angle which makes the move toward the interior of the feasible region.

Multiple change-points detection in high dimension

2019 ◽  
Vol 08 (04) ◽  
pp. 1950014 ◽  
Author(s):  
Yunlong Wang ◽  
Changliang Zou ◽  
Zhaojun Wang ◽  
Guosheng Yin
Keyword(s):  
Dynamic Programming Algorithm ◽  
Null Distribution ◽  
Real Data ◽  
Information Criterion ◽  
Change Point Detection ◽  
New Method ◽  
Change Points ◽  
Estimation Accuracy ◽  
Programming Algorithm ◽  
Order Structure

Change-point detection is an integral component of statistical modeling and estimation. For high-dimensional data, classical methods based on the Mahalanobis distance are typically inapplicable. We propose a novel testing statistic by combining a modified Euclidean distance and an extreme statistic, and its null distribution is asymptotically normal. The new method naturally strikes a balance between the detection abilities for both dense and sparse changes, which gives itself an edge to potentially outperform existing methods. Furthermore, the number of change-points is determined by a new Schwarz’s information criterion together with a pre-screening procedure, and the locations of the change-points can be estimated via the dynamic programming algorithm in conjunction with the intrinsic order structure of the objective function. Under some mild conditions, we show that the new method provides consistent estimation with an almost optimal rate. Simulation studies show that the proposed method has satisfactory performance of identifying multiple change-points in terms of power and estimation accuracy, and two real data examples are used for illustration.

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