{"componentChunkName":"component---src-templates-course-unit-page-tsx","path":"/en/courseunit/031025a/","result":{"data":{"translations":{"edges":[{"node":{"context":{"locale":"fi","code":"031025A","title":"Optimoinnin perusteet"},"path":"/fi/opintojakso/031025a/"}},{"node":{"context":{"locale":"en","code":"031025A","title":"Introduction to Optimization"},"path":"/en/courseunit/031025a/"}}]},"SISU":{"courseUnit":[{"id":"otm-f0fcbf6a-4567-358f-9d19-9071e6a7db0b","code":"031025A","name":{"en":"Introduction to Optimization","fi":"Optimoinnin perusteet","sv":"Optimoinnin perusteet"},"credits":{"max":5,"min":5},"studyLevel":null,"possibleAttainmentLanguages":[{"name":{"en":"English","fi":"englanti","sv":"engelska"}},{"name":{"en":"Finnish","fi":"suomi","sv":"finska"}}],"responsibleOrganisations":[],"coordinatingOrganisations":[],"curriculumPeriods":[],"cooperationNetworkDirection":"INBOUND","cooperationNetworks":[{"targetGroups":[{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["jy-DP-21321","jy-DP-13215","otm-157daa3c-6f87-4d1d-86e2-5f2ed9872b58","jy-DP-13221","jy-DP-21280"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["jy-DP-15471","jy-DP-13215"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-af81f116-e2c7-4ddd-a995-b5a3f769efd0"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-7115fcfa-a836-4071-87dd-12907142ff6e"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-d4ca8e88-2100-4732-9b27-613c74807e98"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-56907236-443b-46cc-82cd-4f5f900be109"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"phase2OptionGroupIds":null,"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase2OptionChildGroupIds":null,"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null},{"activePhase":null,"educationIds":null,"educationTypes":null,"organisationIds":null,"educationGroupIds":null,"phase1OptionGroupIds":null,"phase2OptionGroupIds":["otm-141caed2-2906-4382-8115-8a32f8aea2d9"],"parentOrganisationIds":null,"learningOpportunityIds":null,"phase1OptionChildGroupIds":null,"phase2OptionChildGroupIds":["otm-a1152c89-5848-4824-b84c-d9b9366c8de3"],"phase1EducationClassificationUrns":null,"phase2EducationClassificationUrns":null}],"description":{"en":"<p>This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:</p><ul><li>Bachelor's Degree Programme in Mathematics</li><li>Master's Degree Programme in Mathematics</li><li>Bachelor's Degree Programme in Mathematics (Subject Teacher)</li><li>Master's Degree Programme in Mathematics&nbsp;(Subject Teacher)</li><li>Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)</li><li>Doctoral Programme in Mathematics and Statistics</li><li>Doctoral Programme in Mathematics and Science (Specialication in Mathematics)</li><br></ul>","fi":"<p>Tämä opintojakso on tarjolla Matematiikan syventävät opinnot -ristiinopiskeluverkostossa. Verkoston opinnot ovat tarjolla seuraaville opiskelijoille:</p><ul><li>Matematiikan kandidaattiohjelma</li><li>Matematiikan maisteriohjelma</li><li>Matematiikan aineenopettajien kandidaattiohjelma</li><li>Matematiikan aineenopettajien maisteriohjelma</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan kandidaattiohjelma (matematiikan opintosuunta)</li><li>Matematiikan, kemian tai fysiikan aineenopettajan ja luokanopettajan maisteriiohjelma (matematiikan opintosuunta)</li><li>Matematiikan ja tilastotieteen tohtoriohjelma</li><li>Matemaattisten tieteiden ja luonnontieteiden tohtoriohjelma (matematiikan opintosuunta)</li><br></ul>"},"cooperationNetwork":{"abbreviation":"matematiikansyventavat","name":{"en":"Cross-institutional studies in advanced courses in mathematics and statistics","fi":"Matematiikan ja tilastotieteen syventävien kurssien ristiinopiskelu","sv":"Korsstudier i fördjupade kurser i matematik och statistik"}}}],"gradeScaleId":"sis-0-5","outcomes":{"en":"After completing the course  \r\n- student can classify optimization problems and knows basic optimization algorithms for solving them.  \r\n- student is can formulate the necessary and sufficient conditions for optimality.","fi":"After completing the course  \r\n- student can classify optimization problems and knows basic optimization algorithms for solving them.  \r\n- student is can formulate the necessary and sufficient conditions for optimality."},"tweetText":null,"content":{"en":"Optimality criteria for unconstrained problems, convexity, gradient descent methods, Newton&#39;s and quasi Newton&#39;s method, least squares problems, KKT-conditions for constrained optimization, second order conditions in constrained optimization, simplex method for linear programming problems, duality in optimization.","fi":"Optimality criteria for unconstrained problems, convexity, gradient descent methods, Newton&#39;s and quasi Newton&#39;s method, least squares problems, KKT-conditions for constrained optimization, second order conditions in constrained optimization, simplex method for linear programming problems, duality in optimization."},"additional":{"en":"Timing  \r\nPeriod 2  \r\n  \r\nTarget group  \r\nThe target group includes, but is not restricted to,  students who need to know practical optimization techniques in applied mathematics, such as the students in Wireless Communication Engineering and Computer Science Engineering.","fi":"Ajoitus  \r\nPeriod 2  \r\n  \r\nKohderyhmä  \r\nThe target group includes, but is not restricted to,  students who need to know practical optimization techniques in applied mathematics, such as students in Wireless Communication Engineering and Computer Science Engineering."},"prerequisites":{"en":"Prerequisites   \r\nCalculus I, Calculus II and Matrix Algebra. Numerical linear algebra course is highly recommended.","fi":"Esitietovaatimukset  \r\nMatematiikan peruskurssit I ja II sekä matriisialgebra. Numeerisia menetelmiä sekä Numeerista  matriisilaskentaa suositellaan suoritetuksi ennen kurssille osallistumista."},"compulsoryFormalPrerequisites":[],"recommendedFormalPrerequisites":[],"literature":[],"learningMaterial":null,"completionMethods":[]}],"prerequisiteCourseUnit":[],"prerequisiteModule":[]},"prerequisiteCourseUnitPage":{"nodes":[]},"prerequisiteModulePage":{"nodes":[]},"parentModulePage":{"nodes":[]}},"pageContext":{"type":"courseUnit","locale":"en","title":"Introduction to Optimization","id":"otm-f0fcbf6a-4567-358f-9d19-9071e6a7db0b","code":"031025A","prerequisiteCourseUnitIds":[],"prerequisiteModuleIds":[],"parentModuleIds":[],"curriculumPeriodStartDate":"2026-08-01","curriculumPeriodEndDate":"2027-08-01","coordinatingOrgIds":[],"searchable":false,"searchTags":null,"organisationIds":["otm-71fd8cc0-9fb4-38e1-bbb0-d1d63f911ddf"],"organisations":[],"attainmentLanguages":["en","fi"],"hasSummerStudies":false,"teachingPeriods":[],"cooperationNetworkDirection":"INBOUND","hasCooperationNetworkSettings":true,"hasAvoinTeaching":false}}}