Management Teoria transmisiunii informatiilor Biologie Didactica Mecanica Literatura comparata Arheologie industriala Politologie Ergoterapie Istoria secolului XX Logopedie CIA Fiscalitate Chimie Informatica AutoCAD Fizica Logistica Marketing Oracle EXPERT ACHIZITII PUBLICE Marketing Psihologie Educationala transporturi Gestiune hoteliera Arhitectura peisagera Comert IS Economia si Gestiunea Intreprinderii I I T M Diverse Transmisiuni Analogice si Digitale. Structuri de date si algoritmi C++ Sociologia Comunicarii in Masa Prelucrarea semnalelor si imaginilor Finante Analiza matematica Algoritmi si programare Metodologie si Statistica Introducere in istoria dreptului Analiza economico financiara Constructii Metodologie Psihologie Cibernetica Electronica industriala Drept constitutiv Comunicare Teoria Sistemelor Frigotehnie Baze de Date Drept comercial Contabilitate Administratie Publica Depanare PC Sociologie Franceza Automatica Drept penal Credit si banci Relatii internationale Ginecologie Drept european Drept Filosofie Istoria literaturii romane Dreptul familiei Educatie fizica si sport Radiologie Pedagogie Sociala Statistica Turism Pedagogie Moneda Credit Istorie Dispozitive si Circuite Electronice Asistenta Sociala Retele de calculatoare SPICE Word Merceologie Drept civil Materiale in electronica Engleza Spectroscopie si LASERI Psihiatrie Visual Basic Consiliere scolara Electronica Mass media Terapia ocupationala si ergoterapia Kinetoterapie Semiotica Medicina Economie Istoria dreptului Managementul resurselor umane Bazele Managementului Industrial Sociologia familiei Limba Romana Circuite digitale integrate Criminalistica Geografie Hidrologie Drept constitutional Contabilitate bancara Astrologie Istoria relatiilor internationale MANAGER DE PROIECT Drept Penal Special Drept economic Programare orientata pe obiecte Relatii Internationale si Studii Europene Teologie Drept administrativ Economie politica Asistenta medicala Internet Fotografia digitala Inginerie mecanica Drept roman Muzica Arhitectura Circuite Integrate Astronomie Bazele Sistemelor de Achizitie a Datelor Protectia Mediului PHP si SQL Prelucrarea si Analiza Imaginilor Matematica SPSS Genetica Psihopedagogie Speciala Agricultura Java

Convex Optimization I

Publicat: 19 Apr 2011 00:00

By Stephen Boyd - Stanford University
Licence:

Course Description:
Concentrates on recognizing and solving convex optimization problems that arise in engineering.Topics include: Convex sets, functions, and optimization problems. Basics of convex analysis. Least-squares, linear and quadratic programs, semidefinite programming, minimax, extremal volume, and other problems. Optimality conditions, duality theory, theorems of alternative, and applications. Interiorpoint methods. Applications to signal processing, control, digital and analog circuit design, computational geometry, statistics, and mechanical engineering.Prerequisites: Good knowledge of linear algebra. Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.
Lectures:








Lecture 1 - Introduction to Convex Optimization I



Introduction, Examples, Solving Optimization Problems, Least-Squares, Linear Programming, Convex Optimizations, How To Solve?, Course Goals












Lecture 2 - Guest Lecturer: Jacob Mattingley



Guest Lecturer: Jacob Mattingley, Logistics, Agenda, Convex Set, Convex Cone, Polyhedra, Positive Semidefinite Cone, Operations That Preserve Convexity, Intersection, Affine Function, Generalized Inequalities, Minimum And Minimal Elements, Supporting Hyperlane Theorem, Minimum And Minimal Elements Via Dual Inequalities












Lecture 3 - Logistics



Logistics, Convex Functions, Examples, Restriction Of A Convex Function To A Line, First-Order Condition, Examples (FOC And SOC), Epigraph And Sublevel Set, Jensen's Inequality, Operations That Preserve Convexity, Pointwise Maximum, Pointwise Maximum, Composition With Scalar Functions, Vector Composition












Lecture 4 - Vector Composition



Vector Composition, Perspective, The Conjugate Function, Quasiconvex Functions, Examples, Properties (Of Quasiconvex Functions), Log-Concave And Log-Convex Functions, Properties (Of Log-Concave And Log-Convex Functions), Examples (Of Log-Concave And Log-Convex Functions)












Lecture 5 - Optimal And Locally Optimal Points



Optimal And Locally Optimal Points, Feasibility Problem, Convex Optimization Problem, Local And Global Optima, Optimality Criterion For Differentiable F0, Equivalent Convex Problems, Quasiconvex Optimization, Problem Families, Linear Program












Lecture 6 - (Generalized) Linear-Fractional Program



(Generalized) Linear-Fractional Program, Quadratic Program (QP), Quadratically Constrained Quadratic Program (QCQP), Second-Order Cone Programming, Robust Linear Programming, Geometric Programming, Example (Design Of Cantilever Beam), GP Examples (Minimizing Spectral Radius Of Nonnegative Matrix)












Lecture 7 - Generalized Inequality Constraints



Generalized Inequality Constraints, Semidefinite Program (SDP), LP And SOCP As SDP, Eigenvalue Minimization, Matrix Norm Minimization, Vector Optimization, Optimal And Pareto Optimal Points, Multicriterion Optimization, Risk Return Trade-Off In Portfolio Optimization, Scalarization, Scalarization For Multicriterion Problems












Lecture 8 - Lagrangian



Lagrangian, Lagrange Dual Function, Least-Norm Solution Of Linear Equations, Standard Form LP, Two-Way Partitioning, Dual Problem, Weak And Strong Duality, Slater's Constraint Qualification, Inequality Form LP, Quadratic Program, Complementary Slackness












Lecture 9 - Complementary Slackness



Complementary Slackness, Karush-Kuhn-Tucker (KKT) Conditions, KKT Conditions For Convex Problem, Perturbation And Sensitivity Analysis, Global Sensitivity Result, Local Sensitivity, Duality And Problem Reformulations, Introducing New Variables And Equality Constraints, Implicit Constraints, Semidefinite Program












Lecture 10 - Applications Section of Course



Applications Section Of The Course, Norm Approximation, Penalty Function Approximation, Least-Norm Problems, Regularized Approximation, Scalarized Problem, Signal Reconstruction, Robust Approximation, Stochastic Robust LS, Worst-Case Robust LS












Lecture 11 - Statistical Estimation



Statistical Estimation, Maximum Likelihood Estimation, Examples, Logistic Regression, (Binary) Hypothesis Testing, Scalarization, Experiment Design, D-Optimal Design












Lecture 12 - Continue On Experiment Design



Continue On Experiment Design, Geometric Problems, Minimum Volume Ellipsoid Around A Set, Maximum Volume Inscribed Ellipsoid, Efficiency Of Ellipsoidal Approximations, Centering, Analytic Center Of A Set Of Inequalities, Linear Discrimination












Lecture 13 - Linear Discrimination (Cont.)



Linear Discrimination (Cont.), Robust Linear Discrimination, Approximate Linear Separation Of Non-Separable Sets, Support Vector Classifier, Nonlinear Discrimination, Placement And Facility Location, Numerical Linear Algebra Background, Matrix Structure And Algorithm Complexity, Linear Equations That Are Easy To Solve, The Factor-Solve Method For Solving Ax = B, LU Factorization












Lecture 14 - LU Factorization (Cont.)



LU Factorization (Cont.), Sparse LU Factorization, Cholesky Factorization, Sparse Cholesky Factorization, LDLT Factorization, Equations With Structured Sub-Blocks, Dominant Terms In Flop Count, Structured Matrix Plus Low Rank Term












Lecture 15 - Algorithm Section Of The Course



Algorithm Section Of The Course, Unconstrained Minimization, Initial Point And Sublevel Set, Strong Convexity And Implications, Descent Methods, Gradient Descent Method, Steepest Descent Method, Newton Step, Newton's Method, Classical Convergence Analysis, Examples












Lecture 16 - Continue On Unconstrained Minimization



Continue On Unconstrained Minimization, Self-Concordance, Convergence Analysis For Self-Concordant Functions, Implementation, Example Of Dense Newton System With Structure, Equality Constrained Minimization, Eliminating Equality Constraints, Newton Step, Newton's Method With Equality Constraints












Lecture 17 - Newton's Method (Cont.)



Newton's Method (Cont.), Newton Step At Infeasible Points, Solving KKT Systems, Equality Constrained Analytic Centering, Complexity Per Iteration Of Three Methods Is Identical, Network Flow Optimization, Analytic Center Of Linear Matrix Inequality, Interior-Point Methods, Logarithmic Barrier












Lecture 18 - Logarithmic Barrier



Logarithmic Barrier, Central Path, Dual Points On Central Path, Interpretation Via KKT Conditions, Force Field Interpretation, Barrier Method, Convergence Analysis, Examples, Feasibility And Phase I Methods












Lecture 19 - Interior-Point Methods (Cont.)



Interior-Point Methods (Cont.), Example, Barrier Method (Review), Complexity Analysis Via Self-Concordance, Total Number Of Newton Iterations, Generalized Inequalities, Logarithmic Barrier And Central Path, Barrier Method, Course Conclusion, Further Topics





Source: http://academicearth.org/courses/convex-optimization-i

Trebuie sa citesti

Pictorul Fericit - primele elemente pentru a dezvolta un hobby
Pictorul Fericit - primele elemente pentru a dezvolta un hobby

Hobby-urile sunt cele care ne mentin activi de cele mai multe ori. Punctele de interes si motivatiile stau de cele mai multe ori in lucruri marunte. Uneori se merita sa muncesti cand stii ca la finalul orelor de munca ai parte de momentul tau preferat din zi, cand te ocupi de pasiunea ta. Printre

Ce trebuie sa stii inainte sa iti pui aparat dentar? Iata cate tipuri exista!
Ce trebuie sa stii inainte sa iti pui aparat dentar? Iata cate tipuri exista!

Tratamentul ortodontic implica utilizarea unui aparat dentar special conceput pentru a aplica presiune asupra dintilor si a-i aduce in pozitia corespunzatoare, a corecta muscatura si a imbunatati sanatatea bucala. Acest dispozitiv se poarta pe o perioada de unul sau doi ani, in functie de

Reduceri semnificative la numeroase modele de saltea yoga!
Reduceri semnificative la numeroase modele de saltea yoga!

Indiferent daca esti incepator sau avansat in aceasta practica straveche, cu accesoriile potrivite, sedintele de asane se pot schimba considerabil, devenind mai eficiente! Si, pentru ca acum poti gasi reduceri atractive la numeroase modele de saltea yoga si alegerea poate fi coplesitoare, iata

Apartamente in regim hotelier - cazarea ideala pentru studenti
Apartamente in regim hotelier - cazarea ideala pentru studenti

Înscrierea la facultate se apropie cu pași repezi iar elevii au început deja să își aleagă universitatea unde doresc să își continue studiile. București se află printre preferințele acestora datorită prestigiului pe care îl

Metodele eficiente care te tin in siguranta cand pleci la drum lung
Metodele eficiente care te tin in siguranta cand pleci la drum lung

Fie ca trebuie sa te deplasezi in vacanta, in afara orasului sau sa iti vizitezi rudele si sa pleci la drum lung, trebuie sa te pregatesti din toate punctele de vedere, ca sa ajungi cu bine la destinatie. Deci, ai nevoie de cateva masuri de precautie, in timp ce tii cont de anumite aspecte

Teste Online

Ce culoare te caracterizeaza?

Acest test va va arata curoarea care te caracterizeaza.

mai multe »