Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Regression Analysis01:11

Regression Analysis

7.4K
Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
7.4K
Response Surface Methodology01:16

Response Surface Methodology

472
Response Surface Methodology (RSM) is a collection of statistical and mathematical techniques used to develop, improve, and optimize processes. It is particularly valuable when many input variables or factors potentially influence a response variable.
The process of RSM involves several key steps:
472
Study Design in Statistics01:15

Study Design in Statistics

9.8K
A study design is a set of techniques that allow a researcher to collect and analyze data from different variables defined for a specific research problem. Statistics is commonly for effective study design and more robust experiments,
Does aspirin reduce the risk of heart attacks? Is one brand of fertilizer more effective at growing roses than another? Is fatigue as dangerous to a driver as the influence of alcohol? Questions like these are answered using randomized experiments with proper...
9.8K
Multiple Regression01:25

Multiple Regression

3.6K
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
3.6K
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

8.7K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
8.7K
Bioequivalence Experimental Study Designs: Repeated Measures, Cross-Over, Carry-Over, and Latin Square Designs01:15

Bioequivalence Experimental Study Designs: Repeated Measures, Cross-Over, Carry-Over, and Latin Square Designs

90
Body:Bioequivalence experimental study designs play a pivotal role in testing the effectiveness of various treatments. Key among these are the repeated measures, cross-over, carry-over, and Latin square designs. In the repeated measures design, each subject receives all treatments, allowing for temporal comparisons. This type of design is useful in reducing variability but requires careful planning to avoid bias.The cross-over design, an economical method, involves sequential administration of...
90

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Dysbiotic microbiota trigger colitis-associated colorectal cancer and imprint a distinctive bile acid profile in a PSC-IBD model.

Gut·2026
Same author

Optimal designs for discrete-time survival models with competing risks.

Lifetime data analysis·2026
Same author

Two-level non-regular fractional factorial designs for public health studies.

BMC medical research methodology·2026
Same author

Minimax optimal designs via particle swarm optimization methods.

Statistics and computing·2025
Same author

An Efficient Way to Find Optimal Crossover Designs Using CVX for Precision Medicine.

Journal of data science, statistics, and visualisation·2025
Same author

Nature-inspired metaheuristics for optimizing dose-finding and computationally challenging clinical trial designs.

Clinical trials (London, England)·2025

Related Experiment Video

Updated: Dec 6, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

5.5K

Using SeDuMi to find various optimal designs for regression models.

Weng Kee Wong1, Yue Yin2, Julie Zhou2

  • 1Department of Biostatistics, University of California, Los Angeles, CA 90095-1772, USA.

Statistical Papers (Berlin, Germany)
|October 5, 2020
PubMed
Summary

This study introduces semidefinite programming (SDP) as an effective numerical tool for optimization problems. It demonstrates SDP

Keywords:
Approximate designconvex optimizationequivalence theoremnonlinear modelweighted least squares

More Related Videos

Optimization of the Epimedii Folium Mutton-Oil Processing Technology and Testing Its Effect on Zebrafish Embryonic Development
06:00

Optimization of the Epimedii Folium Mutton-Oil Processing Technology and Testing Its Effect on Zebrafish Embryonic Development

Published on: March 17, 2023

728
Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

17.0K

Related Experiment Videos

Last Updated: Dec 6, 2025

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM
13:54

A Workflow for Lipid Nanoparticle LNP Formulation Optimization using Designed Mixture-Process Experiments and Self-Validated Ensemble Models SVEM

Published on: August 18, 2023

5.5K
Optimization of the Epimedii Folium Mutton-Oil Processing Technology and Testing Its Effect on Zebrafish Embryonic Development
06:00

Optimization of the Epimedii Folium Mutton-Oil Processing Technology and Testing Its Effect on Zebrafish Embryonic Development

Published on: March 17, 2023

728
Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study
20:24

Characterization of Complex Systems Using the Design of Experiments Approach: Transient Protein Expression in Tobacco as a Case Study

Published on: January 31, 2014

17.0K

Area of Science:

  • Statistics and Optimization
  • Numerical Analysis
  • Engineering Applications

Background:

  • Optimization problems with discretized search spaces are common across scientific disciplines.
  • Semidefinite programming (SDP) is a powerful but underutilized numerical method for solving these problems.
  • Optimal design problems are critical in statistical modeling and experimental planning.

Purpose of the Study:

  • To introduce and demonstrate the application of semidefinite programming (SDP) using SeDuMi in MATLAB for optimal design problems.
  • To showcase the flexibility of SDP in handling various optimal design criteria (A-, A-, c-, I-, L-optimality).
  • To extend the application of SDP to optimal designs involving weighted least squares estimators and constrained weight distributions.

Main Methods:

  • Formulation of optimal design problems (A-, A-, c-, I-, L-optimal) as SDP problems.
  • Utilizing the SeDuMi (self-dual minimization) solver in MATLAB for solving the formulated SDPs.
  • Application of the Kiefer-Wolfowitz equivalence theorem for verifying the optimality of approximate designs.
  • Extension to nonlinear regression models and constrained optimization scenarios.

Main Results:

  • Successful formulation and solution of various optimal design problems using SDP and SeDuMi.
  • Demonstrated flexibility of the SDP approach for weighted least squares and constrained designs.
  • Verification of optimality for approximate designs using established statistical theorems.
  • Application to both linear and nonlinear regression models, including those in social and biomedical research.

Conclusions:

  • Semidefinite programming offers a powerful and versatile numerical approach for solving a wide range of optimal design problems.
  • SeDuMi provides an effective tool for implementing SDP solutions in MATLAB for statistical optimal design.
  • The SDP methodology is applicable to complex scenarios, including nonlinear models and designs with specific constraints.