6_search_in_continuous_space by royaghavami · Pull Request #11 · sut-ai/notes

royaghavami · 2021-10-31T10:03:12Z

No description provided.

nimajam41 · 2021-11-01T12:35:56Z

notebooks/6_search_in_continuous_spaces/index.md

+Search in Continuous Space
+#
+# **Table of Contents**
+` `**TOC \o "1-3" \h \z \u [Introduction	 PAGEREF _Toc86421092 \h 2**](#_Toc86421092)**


Your PAGEREFs seem to have some problems when I view the maekdown.

nimajam41 · 2021-11-01T12:39:02Z

notebooks/6_search_in_continuous_spaces/index.md

+# **Table of Contents**
+` `**TOC \o "1-3" \h \z \u [Introduction	 PAGEREF _Toc86421092 \h 2**](#_Toc86421092)**
+
+[**Type of optimization techniques	 PAGEREF _Toc86421093 \h 2**](#_Toc86421093)


"Types" is better

nimajam41 · 2021-11-01T12:52:00Z

notebooks/6_search_in_continuous_spaces/index.md

+#
+
+
+# Introduction


You can provide some examples of optimization problems that can help readers to understand the significance of this topic. (check out slides)

nimajam41 · 2021-11-01T13:05:44Z

notebooks/6_search_in_continuous_spaces/index.md

+## Constrained optimization and Unconstrained optimization 
+**Constrained optimization problems** consider the problem of optimizing an objective function subject to constraints on the variables. In general terms,
+
+minimize fx


Try to use LaTeX for equations (or if it's hard to use LaTeX in markdown, use screenshots of LaTeX equations)

nimajam41 · 2021-11-01T13:09:24Z

notebooks/6_search_in_continuous_spaces/index.md

+
+We denote the set of points for which all the constraints are satisfied as C, and say that any x ∈ C (resp. x ∈/ C) is feasible (resp. infeasible)
+
+***Unconstrained optimization problems*** the answers are constrained into being subject of set C as the picture bellow shows: 


Try to avoid using different formats in a section. For example "Constrained optimization and Unconstrained optimization" is just bold while "Unconstrained optimization problems" is in bold and italics.

nimajam41 · 2021-11-01T13:12:13Z

notebooks/6_search_in_continuous_spaces/index.md

+### Cost functions
+In many cases, particularly economics the cost function which is the objective function of an optimization problem is non-differentiable. These non-smooth cost functions may include discontinuities and discontinuous gradients and are often seen in discontinuous physical processes. Optimal solution of these cost functions is a matter of importance to economists but presents a variety of issues when using numerical methods thus leading to the need for special solution methods.
+
+In this lecture we don’t discuss non-differential optimization and non-smooth functions and the text above was for introduction and further information on this topic.


Try to reformat this sentence and provide at least a reference for further information.

nimajam41 · 2021-11-01T13:16:22Z

notebooks/6_search_in_continuous_spaces/index.md

+
+fαx+1-αy≤αfx+1-αfy (\*)
+
+*Figure  SEQ Figure \\* ARABIC 3. In convex function f, for every two point x,y∈domainf, the line segment between them lies above the graph of f.*


This figure went into your other texts which is not desirable

nimajam41 · 2021-11-01T13:23:18Z

notebooks/6_search_in_continuous_spaces/index.md

+Such a problem may have multiple feasible regions and multiple locally optimal points within each region.  It can take time exponential in the number of variables and constraints to determine that a non-convex problem is infeasible, that the objective function is unbounded, or that an optimal solution is the "global optimum" across all feasible regions.
+##
+## Local and global optimization:
+### Local optimization 


It's better to add examples or some figures which can show the difference between these two concepts

nimajam41 · 2021-11-01T13:26:12Z

notebooks/6_search_in_continuous_spaces/index.md

+
+In this lecture we don’t discuss non-differential optimization and non-smooth functions and the text above was for introduction and further information on this topic.
+
+# Convexity


Try to use examples of convex/non-convex sets/functions and proof why they are convex/non-convex.

Some examples are provided, but use other examples and prove them by definition.

nimajam41

Some major problems:

Try to provide some examples in different sections to help readers understand each concept.
Review your output file to revise some markdown problems.
Use markdown capabilities or LaTeX to write mathematical equations in a better format

nimajam41 · 2021-11-21T11:44:34Z

notebooks/6_search_in_continuous_spaces/index.md

+
+Search in Continuous Space
+#
+# **Table of Contents**


Try to use the same format throughout this part, if you start your words with uppercase letters then do the same for other words.

nimajam41 · 2021-11-21T13:43:57Z

notebooks/6_search_in_continuous_spaces/index.md

+
+![](Aspose.Words.153ba005-881a-4c4b-97e3-6ea90eff943d.003.jpeg)
+
+*Figure  SEQ Figure \\* ARABIC 1. reconstructed image after solving the optimization*


this caption has problem yet

nimajam41 · 2021-11-21T13:50:37Z

notebooks/6_search_in_continuous_spaces/index.md

+
+In unconstrained optimization problems the answers are constrained into being subject of set C as the picture bellow shows: 
+
+*Figure  SEQ Figure \\* ARABIC 2. constrained vs unconstrained optimization*


again problem with figure SEQ

nimajam41 · 2021-11-21T14:19:45Z

notebooks/6_search_in_continuous_spaces/index.md

+## Differentiable optimization and Non-differentiable optimization
+Non-differentiable optimization is a category of optimization that deals with objective that for a variety of reasons is non-differentiable and thus non-convex. The functions in this class of optimization are generally non-smooth. These functions although continuous often contain sharp points or corners that do not allow for the solution of a tangent and are thus non-differentiable. In practice non-differentiable optimization encompasses a large variety of problems and a single one-size fits all solution is not applicable however solution is often reached through implementation of the sub gradient method. Non-differentiable functions often arise in real world applications and commonly in the field of economics where cost functions often include sharp points.
+
+*Figure  SEQ Figure \\* ARABIC 3. Non-differentiable function*


Figure SEQ problem again

nimajam41

Figure numbers have some problems that should be reviewed.

royaghavami added 12 commits October 29, 2021 22:49

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sararajabzadeh requested a review from nimajam41 October 31, 2021 10:05

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royaghavami added 7 commits November 12, 2021 20:54

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royaghavami added 12 commits November 12, 2021 20:56

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		We denote the set of points for which all the constraints are satisfied as C, and say that any x ∈ C (resp. x ∈/ C) is feasible (resp. infeasible)

		*Unconstrained optimization problems* the answers are constrained into being subject of set C as the picture bellow shows:


		fαx+1-αy≤αfx+1-αfy (\*)

		Figure SEQ Figure \\ ARABIC 3. In convex function f, for every two point x,y∈domainf, the line segment between them lies above the graph of f.*


		In this lecture we don’t discuss non-differential optimization and non-smooth functions and the text above was for introduction and further information on this topic.

		# Convexity


		![](Aspose.Words.153ba005-881a-4c4b-97e3-6ea90eff943d.003.jpeg)

		Figure SEQ Figure \\ ARABIC 1. reconstructed image after solving the optimization*


		In unconstrained optimization problems the answers are constrained into being subject of set C as the picture bellow shows:

		Figure SEQ Figure \\ ARABIC 2. constrained vs unconstrained optimization*

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