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Conic optimization information


Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine subspace and a convex cone.

The class of conic optimization problems includes some of the most well known classes of convex optimization problems, namely linear and semidefinite programming.

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Conic optimization

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Conic optimization is a subfield of convex optimization that studies problems consisting of minimizing a convex function over the intersection of an affine...

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Convex optimization

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Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently...

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Mathematical optimization

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generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from...

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Semidefinite programming

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cone. Therefore, SDP is a special case of conic optimization, which is a special case of convex optimization. When the matrix C is diagonal, the inner...

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Conic constant

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In geometry, the conic constant (or Schwarzschild constant, after Karl Schwarzschild) is a quantity describing conic sections, and is represented by the...

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Robust optimization

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Robust optimization is a field of mathematical optimization theory that deals with optimization problems in which a certain measure of robustness is sought...

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List of optimization software

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integer optimization. ModelCenter – a graphical environment for integration, automation, and design optimization. MOSEK – linear, quadratic, conic and convex...

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List of numerical analysis topics

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Linear matrix inequality Conic optimization Semidefinite programming Second-order cone programming Sum-of-squares optimization Quadratic programming (see...

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Generalized conic

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generalized conic has found applications in approximation theory and optimization theory. Among the several possible ways in which the concept of a conic can...

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Map projection

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distances along all other parallels are stretched. Conic projections that are commonly used are: Equidistant conic, which keeps parallels evenly spaced along...

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Immanuel Bomze

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non-linear optimization with an NP-hard complexity, copositive optimization allows a conic reformulation of these hard problems as a linear optimization problem...

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MOSEK

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mixed-integer quadratic, quadratically constrained, conic and convex nonlinear mathematical optimization problems. The applicability of the solver varies...

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James Renegar

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convex conic optimization problems by first-order methods.' His 2001 monograph A Mathematical View of Interior-point Methods in Convex Optimization is intended...

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Matrix completion

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Dimitris; Cory-Wright, Ryan; Pauphilet, Jean (2021). "Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints". Operations Research...

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JuMP

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programming, semidefinite programming, conic optimization, nonlinear programming, and other classes of optimization problems. JuMP provides access to over...

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Linear programming

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programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject...

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Precoding

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18-28, 2004. A. Wiesel, Y.C. Eldar, S. Shamai, Linear precoding via conic optimization for fixed MIMO receivers, IEEE Transactions on Signal Processing,...

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Steiner point

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triangle One of 20 points associated with a given set of six points on a conic; see Pascal's theorem § Hexagrammum Mysticum Steiner tree problem, an algorithmic...

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Existential theory of the reals

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Dimitris; Cory-Wright, Ryan; Pauphilet, Jean (2021), "Mixed-Projection Conic Optimization: A New Paradigm for Modeling Rank Constraints", Operations Research...

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Lanyue

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patched-conic method of trajectory design. The patched-conic method essentially seeks to "patch" together two (Keplerian) two-body ellipses (the conics) at...

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Nose cone design

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(described below) are often much more difficult to create. The sides of a conic profile are straight lines, so the diameter equation is simply: y = x R...

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AMPL

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mathematical notation of optimization problems. This allows for a very concise and readable definition of problems in the domain of optimization. Many modern solvers...

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Definite quadratic form

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{\displaystyle \;c_{1}~.} This bivariate quadratic form appears in the context of conic sections centered on the origin. If the general quadratic form above is...

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Convex cone

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Conditions in Convex Optimization: A Finite-Dimensional View. CRC Press. p. 243. ISBN 9781439868225. Neustadt, Lucien W. (2015-03-08). Optimization: A Theory of...

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General algebraic modeling system

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system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is...

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Midpoint circle algorithm

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Bresenham's line algorithm. The algorithm can be further generalized to conic sections. This algorithm draws all eight octants simultaneously, starting...

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