### Assignments

• CEE 201 gradescope template
• 2024-01-19 - Homework 1 - matlab skills
• 2024-01-26 - Homework 2 - Optimization: search methods
• 2024-02-02 - Homework 3 - Optimization: gradient methods
• 2024-02-09 - Homework 4 - Uncertainty: axioms of probability
• 2024-02-16 - Homework 5 - Uncertainty: probability distributions
• 2024-02-23 - Homework 6 - Uncertainty: monte carlo simulation and regression
• 2024-03-01 - Homework 7 - Uncertainty: confidence intervals, quantiles, hypothesis testing
• 2024-03-08 - Homework 8 - Network systems analyses
• 2024-03-22 - Project 1 - Generate and distribute enough electrical power to meet uncertain demand.
• 2024-04-05 - Project 2 - Optimize a nonlinear 2D truss for uncertain loads.
• 2024-04-19 - Project 3 - Provide enough clean drinking water.
• 2024-04-30 - Final

### matlab functions for optimization

These matlab functions implement methods for minimizing a function of several variables subject to a set of inequality constraints:
minimize f(x) such that g(x) ≤ 0,
where x is a vector of design variables, f(x) is a scalar-valued objective function, and g(x) is a vector of constraints.

• Examples of running constrained minimization codes
• ORSopt.m implements an optimized step-size random search algorithm.
• NMAopt.m implements a Nelder-Mead algorithm.
• SQPopt.m implements a sequential quadratic programming algorithm.
• avg_cov_func.m calculates average and coefficient of variation of a random penalized objective function.
• box_constraint.m determines the box constraint scaling factor a>0 to the perturbation vector r from x such that: max(x+ar) < +1 and min(x+ar) > -1
• optim_options.m is needed for ORSopt.m, NMAopt.m, and SQPopt.m
• plot_surface.m plots the cost function as a surface over two of the parameter values, ORSopt, NMAopt, or SQPopt
• plot_cvg_hst.m plots the convergence history for the solution computed by ORSopt, NMAopt, or SQPopt

### matlab functions for random variables

These matlab functions can be used to compute probability distribution functions and to generate samples of random variables.
 Distribution PDF, fX(x) CDF, FX(x) inverse CDF, FX-1(p) generate sample, x1 ... xN uniform unifpdf.m unifcdf.m unifinv.m rand.m triangular triangular_pdf.m triangular_cdf.m triangular_inv.m triangular_rnd.m quadratic quadratic_pdf.m quadratic_cdf.m quadratic_inv.m quadratic_rnd.m beta beta_pdf.m beta_cdf.m beta_inv.m beta_rnd.m normal norm_pdf.m norm_cdf.m norm_inv.m norm_rnd.m log-normal logn_pdf.m logn_cdf.m logn_inv.m logn_rnd.m Poisson Poisson_pmf.m Poisson_cdf.m Poisson_rnd.m exponential exp_pdf.m exp_cdf.m exp_inv.m exp_rnd.m Rayleigh Rayleigh_pdf.m Rayleigh_cdf.m Rayleigh_inv.m Rayleigh_rnd.m ext I extI_pdf.m extI_cdf.m extI_inv.m extI_rnd.m ext II extII_pdf.m extII_cdf.m extII_inv.m extII_rnd.m gamma gamma_pdf.m gamma_cdf.m gamma_inv.m gamma_rnd.m Laplace Laplace_pdf.m Laplace_cdf.m Laplace_inv.m Laplace_rnd.m GEV GEV_pdf.m GEV_cdf.m GEV_inv.m GEV_rnd.m Chi-squared chi2_pdf.m chi2_cdf.m chi2_inv.m chi2_rnd.m Student's-t t_pdf.m t_cdf.m t_inv.m t_rnd.m

• plotCDFci.m plots the empirical CDF from a sample of data along with the confidence interval of the CDF.
• corr_logn_rnd.m generates a sample of correlated log normal values.
• MCS_intro.m illustrates the use of a number of these functions.

### Outside Reading

© 2001-2020 Henri P. Gavin; updated: 2001-09-27, 2003-12-15, 2004-01-07, 2005-02-14, 2006-01-11, 2009-08-07, 2011-01-05, 2014-01-08, 2015-01-07, 2016-01-13, 2020-01-20, 2024-02-28