CBE60499¶

Index of Figures in this Repository¶

4_1_questions.png¶

4_1_questions.png

  • 4.1.1.3 Key Questions

active_constraints2.png¶

active_constraints2.png

  • 4.3.2 Sensitivity Analysis

active_constraints.png¶

active_constraints.png

  • 4.3.1 Active Sets

alg2-1.png¶

alg2-1.png

  • 3.4.3 Algorithm 2.1: Basic Newton Method

alg3-1.png¶

alg3-1.png

  • 3.5.1 Unconstrained Optimization with Approximate Hessian

Alg3-2.png¶

Alg3-2.png

  • 3.6.3 Line Search

Alg3-3.png¶

Alg3-3.png

  • 3.6.4.1 Main Idea and General Algorithm

alg5-1.png¶

alg5-1.png

  • 4.7 Simple Netwon Method for Equality Constrained NLPs

alg5-2a.png¶

alg5-2a.png

  • 4.8 Inertia-Corrected Netwon Method for Equality Constrained NLPs

alg5-2b.png¶

alg5-2b.png

  • 4.8 Inertia-Corrected Netwon Method for Equality Constrained NLPs

apps_table.png¶

apps_table.png

  • 2.0.2 Taxonomy of Optimization Problems

battery.png¶

battery.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.1.3 Optimization Mathematical Model

casadi-error1.png¶

casadi-error1.png

  • 2.4.3.1 Formulation 1: Index-3 DAE

casadi-error2.png¶

casadi-error2.png

  • 2.4.3.1 Formulation 1: Index-3 DAE

classification.png¶

classification.png

  • 2.0.2 Taxonomy of Optimization Problems

cone1.png¶

cone1.png

  • 4.5 Second Order Optimality Conditions
  • 4.5.1 Helpful Cones

cone2.png¶

cone2.png

  • 4.5 Second Order Optimality Conditions
  • 4.5.1 Helpful Cones

constrained_analysis.png¶

constrained_analysis.png

  • 4.2.3.7 Analysis without Constraints
  • 4.2.3.8 Analysis with Constraints

dae_form1.png¶

dae_form1.png

  • 2.4.2 DAE Index Reduction

dae_form2.png¶

dae_form2.png

  • 2.4.2 DAE Index Reduction

dae_reduction.png¶

dae_reduction.png

  • 2.4.2 DAE Index Reduction

def-4-6.png¶

def-4-6.png

  • 4.3.2 Sensitivity Analysis

def-4-12.png¶

def-4-12.png

  • 4.4.2.2 Linearly Independent Constraint Qualification (LICQ))

def-4-19.png¶

def-4-19.png

  • 4.5.4 Reduced Hessian

def_4_1_a.png¶

def_4_1_a.png

  • 4.1.1.2 Types of Constrained Optimal Solutions

def_4_1_b.png¶

def_4_1_b.png

  • 4.1.1.2 Types of Constrained Optimal Solutions

descent_direction.png¶

descent_direction.png

  • 3.6.2.5 Descent Properties

det.png¶

det.png

  • 3.1.2 Determinant

det_ex1.png¶

det_ex1.png

  • 3.1.2 Determinant

det_ex2.png¶

det_ex2.png

  • 3.1.2 Determinant

dynamic_optimization_strategies.png¶

dynamic_optimization_strategies.png

  • 2.4.1 Dynamic Optimization Overview

eig.png¶

eig.png

  • 3.1.7 Eigenvectors and Eigenvalues

eq_6_56.png¶

eq_6_56.png

  • 4.9.1.1 Background

eq_6_57.png¶

eq_6_57.png

  • 4.9.1.1 Background

eq_6_58.png¶

eq_6_58.png

  • 4.9.1.1 Background

eq_6_59.png¶

eq_6_59.png

  • 4.9.1.1 Background

eqn5-12.png¶

eqn5-12.png

  • 4.8 Inertia-Corrected Netwon Method for Equality Constrained NLPs

errata_83.png¶

errata_83.png

  • 4.5.5 Example

ex2-19.png¶

ex2-19.png

  • 3.3.4 Example 2.19 in Biegler (2010))
  • 3.4.1 Test Problem: Example 2.19
  • 3.5.3 Test Case: Example 2.19
  • 3.9.3.4 Return of Example 2.19

ex-4-7.png¶

ex-4-7.png

  • 4.3.2 Sensitivity Analysis

ex-4-7b.png¶

ex-4-7b.png

  • 4.3.2 Sensitivity Analysis

ex-4-20.png¶

ex-4-20.png

  • 4.5.5 Example

feasible.png¶

feasible.png

  • 2.2 Integer Programs
  • 2.2.2.4 Why rounding does not always work

general_nlp.png¶

general_nlp.png

  • 4.1.1.1 Canonical Nonlinear Program

imt1.png¶

imt1.png

  • 3.1.6 Invertable Matrix Theorem

imt2.png¶

imt2.png

  • 3.1.6 Invertable Matrix Theorem

imt3.png¶

imt3.png

  • 3.1.6 Invertable Matrix Theorem

imt4.png¶

imt4.png

  • 3.1.6 Invertable Matrix Theorem

inv.png¶

inv.png

  • 3.1.4 Inverse

ip_bounds_G.png¶

ip_bounds_G.png

  • 4.9.1.2 Problem Formulation

kkt_1.png¶

kkt_1.png

  • 4.2.2 Karush-Kuhn-Tucker (KKT) Necessary Conditions-Necessary-Conditions)

kkt_2.png¶

kkt_2.png

  • 4.2.2 Karush-Kuhn-Tucker (KKT) Necessary Conditions-Necessary-Conditions)

limiting_directions.png¶

limiting_directions.png

  • 4.4.1.1 Concepts

linear-opt-4-3.png¶

linear-opt-4-3.png

  • 4.4.1.2 Linear Constrainted Optimization Problems
  • 4.4.2.1 Nonlinear Constrained Optimization Problems

linesearch_conditions.png¶

linesearch_conditions.png

  • 3.6.3 Line Search

LM-TR.png¶

LM-TR.png

  • 3.6.4.2.1 Levenburg-Marquardt

logical_modeling1.png¶

logical_modeling1.png

  • 2.3.1 Logical Modeling

logical_modeling2.png¶

logical_modeling2.png

  • 2.3.1 Logical Modeling

logical_rules.png¶

logical_rules.png

  • 2.3.1 Logical Modeling

mat_op1.png¶

mat_op1.png

  • 3.1.1 Notation (for textbook))

mat_op2.png¶

mat_op2.png

  • 3.1.1 Notation (for textbook))

minlp.png¶

minlp.png

  • 2.0.2 Taxonomy of Optimization Problems

nlp_book_cover.jpg¶

nlp_book_cover.jpg

  • 2.0.1 Recommended Reading

nonlinear-opt-4-3.png¶

nonlinear-opt-4-3.png

  • 4.4.2.1 Nonlinear Constrained Optimization Problems

nonlinear-opt-4-3b.png¶

nonlinear-opt-4-3b.png

  • 4.4.2.1 Nonlinear Constrained Optimization Problems

norm1.png¶

norm1.png

  • 3.1.9 Vector and Matrix Norms

norm2.png¶

norm2.png

  • 3.1.9 Vector and Matrix Norms

pack1.png¶

pack1.png

  • 2.1 Continuous Optimization
  • 2.1.2 Nonlinear Programs: Circle Packing Example
  • 4.1 Convexity Revisited
  • 4.1.3 Circle Packing Example

pack2.png¶

pack2.png

  • 2.1 Continuous Optimization
  • 2.1.2.1 Propose an Optimization Model
  • 4.1 Convexity Revisited
  • 4.1.3.1 Optimization Model and Pyomo Implementation

pack3.png¶

pack3.png

  • 2.1 Continuous Optimization
  • 2.1.2.1 Propose an Optimization Model
  • 4.1 Convexity Revisited
  • 4.1.3.1 Optimization Model and Pyomo Implementation

PD-TR2.png¶

PD-TR2.png

  • 3.6.4.2.2 Powell Dogleg

PD-TR.png¶

PD-TR.png

  • 3.6.4.2.2 Powell Dogleg

projected-reduced-Hessian1.png¶

projected-reduced-Hessian1.png

  • 4.5.4 Reduced Hessian

projected-reduced-Hessian2.png¶

projected-reduced-Hessian2.png

  • 4.5.4 Reduced Hessian

pyomo-table-4.1.png¶

pyomo-table-4.1.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.2.3 Variables

pyomo-table-4.2.png¶

pyomo-table-4.2.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.2.3 Variables

pyomo-table-4.3.png¶

pyomo-table-4.3.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.2.5 Objectives

pyomo-table-4.4.png¶

pyomo-table-4.4.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.2.6 Constraints

pyomo-table-4.6.png¶

pyomo-table-4.6.png

  • 1.1 60 Minutes to Pyomo: An Energy Storage Model Predictive Control Example
  • 1.1.2.4 Parameters (Constants / Data))

pyomo_book_cover.jpg¶

pyomo_book_cover.jpg

  • 2.0.1 Recommended Reading

quad1.png¶

quad1.png

  • 3.2.1 Eigenvalues and Quadratic Programs

rank.png¶

rank.png

  • 3.1.3 Rank

sequential_dae_optimization.png¶

sequential_dae_optimization.png

  • 2.4.1 Dynamic Optimization Overview

strip_packing.png¶

strip_packing.png

  • 2.3 Logical Modeling and Generalized Disjunctive Programs
  • 2.3.2 Pyomo.GDP: Strip Packing Problem

Thm3-3.png¶

Thm3-3.png

  • 3.6.3 Line Search

Thm3-4.png¶

Thm3-4.png

  • 3.6.3 Line Search

thm-4-8.png¶

thm-4-8.png

  • 4.4.1.1 Concepts

thm-4-9.png¶

thm-4-9.png

  • 4.4.1.2 Linear Constrainted Optimization Problems

thm-4-11.png¶

thm-4-11.png

  • 4.4.1.2 Linear Constrainted Optimization Problems

thm-4-14.png¶

thm-4-14.png

  • 4.4.2.2 Linearly Independent Constraint Qualification (LICQ))

thm-4-15.png¶

thm-4-15.png

  • 4.4.2.2 Linearly Independent Constraint Qualification (LICQ))

thm-4-16.png¶

thm-4-16.png

  • 4.4.2.3 Mangasarian-Fromovitz Constraint Qualification (MFCQ))

thm-4-17.png¶

thm-4-17.png

  • 4.5.2 Second Order Necessary Conditions

thm-4-18.png¶

thm-4-18.png

  • 4.5.3 Second Order Sufficient Conditions

thm_4_2.png¶

thm_4_2.png

  • 4.1.2 Convexity for Constrained Optimization

thm_4_3.png¶

thm_4_3.png

  • 4.1.2 Convexity for Constrained Optimization

TR-visual.png¶

TR-visual.png

  • 3.6.4.2 Trust Region Variations

trust-region-intro.png¶

trust-region-intro.png

  • 3.6.4.1 Main Idea and General Algorithm

unconstrained_analysis.png¶

unconstrained_analysis.png

  • 4.2.3.7 Analysis without Constraints

unconstrained_opt.png¶

unconstrained_opt.png

  • 4.2.1 Unconstrained Optimality Conditions