{"id":16742,"date":"2020-02-04T22:49:11","date_gmt":"2020-02-05T03:49:11","guid":{"rendered":"https:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization\/"},"modified":"2020-02-08T09:41:35","modified_gmt":"2020-02-08T14:41:35","slug":"misc-optimization","status":"publish","type":"post","link":"http:\/\/bangla.sitestree.com\/?p=16742","title":{"rendered":"Misc. Optimization:"},"content":{"rendered":"

"Linear programming<\/strong> (LP, also called linear optimization<\/strong>) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear<\/strong> relationships.
\nen.wikipedia.org \u203a wiki \u203a Linear_programming<\/p>\n

<\/a><\/p>\n

<\/a><\/p>\n

Linear programming – Wikipedia<\/a><\/h3>\n

<\/a>"<\/p>\n

"Branch and bound<\/strong> (BB<\/strong>, B&B<\/strong>, or BnB<\/strong>) is an algorithm<\/a> design paradigm<\/a> for discrete<\/a> and combinatorial optimization<\/a> problems, as well as mathematical optimization<\/a>. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search<\/a>: the set of candidate solutions is thought of as forming a rooted tree<\/a> with the full set at the root. The algorithm explores branches<\/em> of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds<\/em> on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm."
\nhttps:\/\/en.wikipedia.org\/wiki\/Branch_and_bound<\/a><\/p>\n

Convex Optimization Branch and Bound Methods<\/strong><\/p>\n

https:\/\/people.orie.cornell.edu\/mru8\/orie6326\/lectures\/sp.pdf<\/a><\/p>\n

Semidefinite Programming and Max-Cut<\/strong><\/p>\n

https:\/\/www.cs.cmu.edu\/~anupamg\/adv-approx\/lecture14.pdf<\/a><\/p>\n

Relating max-cut problems and binary linear feasibility problems<\/strong><\/p>\n

http:\/\/www.optimization-online.org\/DB_FILE\/2009\/02\/2237.pdf<\/a><\/p>\n

"Branch and cut<\/strong>[1]<\/a> is a method of combinatorial optimization<\/a> for solving integer linear programs<\/a> (ILPs), that is, linear programming<\/a> (LP) problems where some or all the unknowns are restricted to integer<\/a> values.[2]<\/a> Branch and cut involves running a branch and bound<\/a> algorithm and using cutting planes<\/a> to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch.<\/strong>"
\nhttps:\/\/en.wikipedia.org\/wiki\/Branch_and_cut<\/a><\/p>\n

Integer Programming<\/strong><\/p>\n

http:\/\/web.mit.edu\/15.053\/www\/AMP-Chapter-09.pdf<\/a><\/p>\n

Bang\u2013bang solutions in optimal control<\/h2>\n

"In optimal control<\/a> problems, it is sometimes the case that a control is restricted to be between a lower and an upper bound. If the optimal control switches from one extreme to the other (i.e., is strictly never in between the bounds), then that control is referred to as a bang-bang solution.
\nBang\u2013bang controls frequently arise in minimum-time problems. For example, if it is desired to stop a car in the shortest possible time at a certain position ahead of the car, the solution is to apply maximum acceleration until the unique switching point<\/em>, and then apply maximum braking to come to rest exactly at the desired position."
\nhttps:\/\/en.wikipedia.org\/wiki\/Bang%E2%80%93bang_control<\/a><\/p>\n

*** . ***
\nNote: Older short-notes from this site are posted on Medium: <\/strong><\/em>https:\/\/medium.com\/@SayedAhmedCanada<\/a><\/p>\n

*** . *** *** . *** . *** . ***
\n<\/em>
\nSayed Ahmed<\/strong>
\n<\/em>
\nBSc. Eng. in Comp. Sc. & Eng. (BUET)<\/strong><\/em>
\nMSc. in Comp. Sc. (U of Manitoba, Canada)<\/strong><\/em>
\nMSc. in Data Science and Analytics (Ryerson University, Canada)<\/strong><\/em>
\nLinkedin<\/strong>: https:\/\/ca.linkedin.com\/in\/sayedjustetc<\/a>
\n<\/em><\/p>\n

Blog<\/strong>: http:\/\/Bangla.SaLearningSchool.com<\/a>, http:\/\/SitesTree.com<\/a><\/em>
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Get access to courses on Big Data, Data Science, AI, Cloud, Linux, System Admin, Web Development and Misc. related. Also, create your own course to sell to others. <\/em>http:\/\/sitestree.com\/training\/<\/a><\/p>\n

I<\/strong>f you want to contribute to occasional free and\/or low cost online\/offline training or charitable\/non-profit work in the education\/health\/social service sector, you can financially contribute to: safoundation at salearningschool.com<\/a> using Paypal or Credit Card (on <\/em>http:\/\/sitestree.com\/training\/enrol\/index.php?id=114<\/a> ).<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

"Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. en.wikipedia.org \u203a wiki \u203a Linear_programming Linear programming – Wikipedia " "Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm … <\/p>\n

Continue reading<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[1910,182],"tags":[],"class_list":["post-16742","post","type-post","status-publish","format-standard","hentry","category-ai-ml-ds-rl-dl-nn-nlp-data-mining-optimization","category---blog","item-wrap"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack-related-posts":[{"id":16689,"url":"http:\/\/bangla.sitestree.com\/?p=16689","url_meta":{"origin":16742,"position":0},"title":"Misc. Math for Data Science, Engineering, and\/or Optimization","author":"Sayed","date":"January 28, 2020","format":false,"excerpt":"What is the Inverse of a Matrix? https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse.html What is Norm? \"In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that satisfies certain properties pertaining to scalability and additivity, and assigns a strictly positive real number to each vector in a vector space over\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16500,"url":"http:\/\/bangla.sitestree.com\/?p=16500","url_meta":{"origin":16742,"position":1},"title":"Overview on optimization concepts: From the Internet","author":"Sayed","date":"December 10, 2019","format":false,"excerpt":"Optimization Concepts: Convex sets: \"A convex set is a set of points such that, given any two points A, B in that set, the line AB joining them lies entirely within that set. Intuitively, this means that the set is connected (so that you can pass between any two points\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16989,"url":"http:\/\/bangla.sitestree.com\/?p=16989","url_meta":{"origin":16742,"position":2},"title":"Modeling and Optimization : Gurobi, Cplex in addition to Matlab","author":"Sayed","date":"April 11, 2020","format":false,"excerpt":"Modeling and Optimization : Gurobi, Cplex in addition to Matlab Python in general can be a better choice for Gurobi, and CPlex. Gurobi works with Matlab as well. You can develop Gurobi applications in Anaconda, and Jupyter. GUROBI OPTIMIZER QUICK START GUIDE https:\/\/www.gurobi.com\/wp-content\/plugins\/hd_documentations\/content\/pdf\/quickstart_linux_8.1.pdf Starting with CPLEX https:\/\/www.ibm.com\/support\/knowledgecenter\/SSSA5P_12.7.1\/ilog.odms.studio.help\/Optimization_Studio\/topics\/COS_home.html https:\/\/www.ibm.com\/support\/knowledgecenter\/SSSA5P_12.7.1\/ilog.odms.cplex.help\/CPLEX\/GettingStarted\/topics\/set_up\/Python_setup.html Gurobi: Reference\u2026","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16967,"url":"http:\/\/bangla.sitestree.com\/?p=16967","url_meta":{"origin":16742,"position":3},"title":"Matlab: Optimization Project Examples","author":"Sayed","date":"March 22, 2020","format":false,"excerpt":"You might want to start with Example Projects or Check examples after some theories. Just digging theories more and more might confuse you (or make things look harder) esp. if your goal is to be eventually able to write code for an optimization project. It might help you to understand\u2026","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":16691,"url":"http:\/\/bangla.sitestree.com\/?p=16691","url_meta":{"origin":16742,"position":4},"title":"Optimization, Data Science, Math","author":"Sayed","date":"January 28, 2020","format":false,"excerpt":"Optimization Problem: Advances in Missile Guidance, Control, and Estimation Preview: https:\/\/play.google.com\/books\/reader?id=A2PMBQAAQBAJ&hl=en_GB&pg=GBS.PR14 https:\/\/books.google.ca\/books?id=A2PMBQAAQBAJ&pg=PA595&lpg=PA595&dq=force+moment+interaction+with+thrusters&source=bl&ots=BruxnXwLzp&sig=ACfU3U39G-l3xDzbotOBJHcMV5uR7DkciQ&hl=en&sa=X&ved=2ahUKEwjZpsT44afnAhXRJt8KHfPYCroQ6AEwCnoECAoQAQ#v=onepage&q=force%20moment%20interaction%20with%20thrusters&f=false \"What is the difference between affine and linear? 4 Answers. A linear function fixes the origin, whereas an affine function need not do so. An affine function is the composition of a linear function with a translation, so\u2026","rel":"","context":"In "AI ML DS RL DL NN NLP Data Mining Optimization"","block_context":{"text":"AI ML DS RL DL NN NLP Data Mining Optimization","link":"http:\/\/bangla.sitestree.com\/?cat=1910"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":63958,"url":"http:\/\/bangla.sitestree.com\/?p=63958","url_meta":{"origin":16742,"position":5},"title":"Misc: Optimization: Machine Learning: Data Science Resources","author":"Sayed","date":"June 3, 2021","format":false,"excerpt":"http:\/\/web.mit.edu\/15.053\/www\/AMP-Chapter-09.pdf https:\/\/www.cs.cmu.edu\/~anupamg\/adv-approx\/lecture14.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization\/ https:\/\/www.futurelearn.com\/info\/courses\/maths-linear-quadratic-relations\/0\/steps\/12128 https:\/\/www.mathsisfun.com\/algebra\/systems-linear-equations-matrices.html https:\/\/www.wolframalpha.com\/input\/?i=subspace https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/notes\/lec3.pdf https:\/\/observablehq.com\/@eliaskal\/point-combinations-linear-conic-affine-convex https:\/\/www.cse.iitk.ac.in\/users\/rmittal\/prev_course\/s14\/course_s14.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-might-relate-to-optimization\/ http:\/\/bangla.salearningschool.com\/recent-posts\/part-x-engineering-optimization-mathematical-optimization\/ https:\/\/www.dr-eriksen.no\/teaching\/GRA6035\/2010\/lecture4.pdf https:\/\/www.mathsisfun.com\/calculus\/concave-up-down-convex.html https:\/\/www-ljk.imag.fr\/membres\/Anatoli.Iouditski\/cours\/convex\/chapitre_3.pdf http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/www.thestudentroom.co.uk\/showthread.php?t=1247928 https:\/\/en.wikipedia.org\/wiki\/Hessian_matrix https:\/\/en.wikipedia.org\/wiki\/Newton%27s_method_in_optimization https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/9781118733639.app6 http:\/\/bangla.salearningschool.com\/recent-posts\/optimization-and-linear-algebra-math-from-the-internet\/ https:\/\/en.wikipedia.org\/wiki\/Interior-point_method https:\/\/web.stanford.edu\/~boyd\/papers\/rt_cvx_sig_proc.html Must Read https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/ivantash-optimization_methods_and_their_applications_in_dsp.pdf https:\/\/www.researchgate.net\/publication\/269211254_The_analysis_and_optimization_algorithms_of_the_electronic_circuits_design good one http:\/\/www.bcamath.org\/documentos_public\/courses\/Nogales_2012-13_02_18-22.pdf https:\/\/en.wikipedia.org\/wiki\/Convex_analysis https:\/\/www.khanacademy.org\/search?page_search_query=Optimization%20problems%20(calculus) http:\/\/bangla.salearningschool.com\/recent-posts\/overview-on-optimization-concepts-from-the-internet\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-optimization-machine-learning\/ http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-data-science-machine-learning-optimization-vector-pca-basis-covariance\/ https:\/\/www.mathsisfun.com\/algebra\/matrix-inverse-row-operations-gauss-jordan.html http:\/\/bangla.salearningschool.com\/recent-posts\/misc-math-for-data-science-engineering-and-or-optimization\/","rel":"","context":"In "\u09ac\u09cd\u09b2\u0997 \u0964 Blog"","block_context":{"text":"\u09ac\u09cd\u09b2\u0997 \u0964 Blog","link":"http:\/\/bangla.sitestree.com\/?cat=182"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16742","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=16742"}],"version-history":[{"count":1,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16742\/revisions"}],"predecessor-version":[{"id":16794,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=\/wp\/v2\/posts\/16742\/revisions\/16794"}],"wp:attachment":[{"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=16742"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=16742"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bangla.sitestree.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=16742"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}