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Convex optimization Assignment help | Convex optimization  Homework help | Convex optimization Online Experts

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It is the study of minimizing the convex functions over convex sets . Following statements of convex optimization problem :
If there is a local minimum then it is considered as global minimum.
Set of all minima is convex .

If the function has minimum then this minimum should be unique.
The usual form in which convex optimization problems are described is termed as its standard form .
It is divided into three parts : convex function , inequality constraints and equality constraints .
Convex function : f(x) : R^n -> R where x is the variable .
Inequality constraints : gi(x) <= 0, where gi is convex.
Equality constraints : It can be described in the form of equation : hi(x) =ai^Tx+bi where ai = column vector and bi = real
number .

Convex optimization problems can be solved by following methods : Bundle method , interior point method , ellipsoid method ,
cutting plane method , subgradient method etc.
Example of convex optimized problem : least squares , linear programming , geometric programming , second order cone
programming , entropy maximization etc.

Basics of convex analysis: Convex setsfunctionsand optimization problems. Optimization theory: Least-squareslinearquadraticgeometric and semidefinite programming. Convex modeling. Duality theory. Optimality and KKT conditions. Applications in signal processingstatisticsmachine learningcontrol communicationsand design of engineering systems

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Topics for Convex optimization  assignment help include :

  • Convex optimization,Convex sets, functions,Basics of convex analysis,Convex optimization problems,Linear and quadratic programming,Second-order cone,Semidefinite programming,Geometric programming,Lagrange duality
  • Optimality conditions,Applications of convex optimization,Unconstrained minimization methods,Interior-point and cutting-plane algorithms,Introduction to nonlinear programming,Convex optimization problems emerging in electrical engineering
  • Efficiently solving convex optimization problems , Use of interior point algorithms software, linear algebra,Convex optimization problems,Duality,Disciplined convex programming,Applications to optimal filtering,Estimation control 

Help for complex topics like :

  • Resources allocations,Sensor network,Distributed systems,Optimization problems,Least-squares
  • Linear quadratic optimization,Geometric programmingsemidefinite programming,Vector optimization
  • Duality theory,Convex relaxations,Fitting, and statistical estimation,Geometic problems,Control and trajectory planning

Convex sets, functions, and optimization problems.
Convex analysis and theory of convex programming: optimality conditions, duality theory, theorems of alternative, and applications.
Least-squares, linear and quadratic programs, semidefinite programming, and geometric programming.
Numerical algorithms for smooth and equality constrained problems;
Interior-point methods for inequality constrained problems.
Applications to signal processing, communications, control, analog and digital circuit design, computational geometry, statistics, machine learning, and mechanical engineering.

Mathematical optimization; least-squares and linear programming; convex optimization; course goals and topics; nonlinear optimization.

Convex sets
Convex sets and cones; some common and important examples; operations that preserve convexity.

Convex functions
Convex functions; common examples; operations that preserve convexity; quasiconvex and log-convex functions.

Convex optimization problems
Convex optimization problems; linear and quadratic programs; second-order cone and semidefinite programs; quasiconvex optimization problems; vector and multicriterion optimization.

Lagrange dual function and problem; examples and applications.

Approximation and fitting
Norm approximation; regularization; robust optimization. (PDF)

Statistical estimation
Maximum likelihood and MAP estimation; detector design; experiment design.

Geometric problems
Projection; extremal volume ellipsoids; centering; classification; placement and location problems.

Filter design and equalization

FIR filters; general and symmetric lowpass filter design; Chebyshev equalization; magnitude design via spectral factorization.

Miscellaneous applications
Multi-period processor speed scheduling; minimum time optimal control; grasp force optimization; optimal broadcast transmitter power allocation; phased-array antenna beamforming; optimal receiver location.

l1 methods for convex-cardinality problems
Convex-cardinality problems and examples; l1 heuristic; interpretation as relaxation.

l1 methods for convex-cardinality problems (cont.)
Total variation reconstruction; iterated re-weighted l1; rank minimization and dual spectral norm heuristic.

Stochastic programming
Stochastic programming; "certainty equivalent" problem; violation/shortfall constraints and penalties; Monte Carlo sampling methods; validation.

Chance constrained optimization
Chance constraints and percentile optimization; chance constraints for log-concave distributions; convex approximation of chance constraints.

Numerical linear algebra background
Basic linear algebra operations; factor-solve methods; sparse matrix methods.

Unconstrained minimization
Gradient and steepest descent methods; Newton method; self-concordance complexity analysis.

Equality constrained minimization
Elimination method; Newton method; infeasible Newton method.

Interior-point methods
Barrier method; sequential unconstrained minimization; self-concordance complexity analysis.

Disciplined convex programming and CVX
Convex optimization solvers; modeling systems; disciplined convex programming; CVX.

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