# Conic Linear Programming

@inproceedings{Luenberger2016ConicLP, title={Conic Linear Programming}, author={D. Luenberger and Y. Ye}, year={2016} }

Conic Linear Programming, hereafter CLP, is a natural extension of Linear programming (LP). In LP, the variables form a vector which is required to be componentwise nonnegative, while in CLP they are points in a pointed convex cone (see Appendix B.1) of an Euclidean space, such as vectors as well as matrices of finite dimensions. For example, Semidefinite programming (SDP) is a kind of CLP, where the variable points are symmetric matrices constrained to be positive semidefinite. Both types of… Expand

#### Figures and Topics from this paper

#### 4 Citations

A New Use of Douglas-Rachford Splitting and ADMM for Identifying Infeasible, Unbounded, and Pathological Conic Programs

- Computer Science, Mathematics
- ArXiv
- 2017

A method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM, which is simple to implement and has low per-iteration cost. Expand

On ambiguity function shaping for broadband constant-modulus signals

- Computer Science
- Signal Process.
- 2020

The advantage of the signal design over conventional unimodular signals for target detection in strong clutter in a continuous active sonar application is demonstrated. Expand

Adaptive Model Predictive Control for Cruise Control of High-Speed Trains with Time-Varying Parameters

- Computer Science
- 2019

It is proved theoretically that, with the proposed adaptive MPC, the high-speed trains track the desired speed with ultimately bounded tracking errors, while the estimated parameters are bounded and the relative spring displacement between the two neighboring cars is stable at the equilibrium state. Expand

Practical measurement-device-independent entanglement quantification

- Physics, Mathematics
- 2017

The robust estimation of entanglement is key to the validation of implementations of quantum systems. On the one hand, the evaluation of standard entanglement measures, either using quantum… Expand

#### References

SHOWING 1-10 OF 362 REFERENCES

Solving Semide nite Programs via Nonlinear Programming

- Mathematics
- 1999

In a semidefinite programming (SDP) problem, a linear function of a symmetric matrix variable X is minimized subject to linear equality constraints on X and the essential constraint that X be… Expand

Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization

- Mathematics, Computer Science
- SIAM J. Optim.
- 1995

It is argued that many known interior point methods for linear programs can be transformed in a mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity carrying over in a similar fashion. Expand

On Cones of Nonnegative Quadratic Functions

- Mathematics, Computer Science
- Math. Oper. Res.
- 2003

It is shown that optimizing a general quadratic function over the intersection of an ellipsoid and a half-plane can be formulated as semidefinite programming (SDP), thus proving the polynomiality of this class of optimization problems, which arise, e.g., from the application of the trust region method for nonlinear programming. Expand

Conic convex programming and self-dual embedding

- Mathematics
- 1998

How ro initialize an algorithm to solve an optimization problem is of great theoretical and practical importance. In the simplex method for linear programming this issue is resolved by either the… Expand

Applications of second-order cone programming

- Mathematics
- 1998

In a second-Order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-Order (quadratic) cones. SOCPs are nonlinear convex Problems that… Expand

Semidefinite programming for assignment and partitioning problems

- Mathematics
- 1998

Semidefinite programming, SDP, is an extension of linear programming, LP, where the nonnegativity constraints are replaced by positive semidefiniteness constraints on matrix variables. SDP has proven… Expand

Geometric Optimization Problems Likely Not Contained in APX

- Mathematics
- 2002

Maximizing geometric functionals such as the classical lp-norms over poly- topes plays an important role in many applications, hence it is desirable to know how efficiently the solutions can be… Expand

Semidefinite Programming

- Computer Science
- SIAM Rev.
- 1996

A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given. Expand

Approximation algorithms for MAX-3-CUT and other problems via complex semidefinite programming

- Mathematics, Computer Science
- STOC '01
- 2001

An extension of semidefinite programming to complex space to solve the natural relaxation, and a natural extension of the random hyperplane technique introduced by the authors to obtain near-optimal solutions to the problems. Expand

Solving Semidefinite Programs via Nonlinear Programming, Part II: Interior Point Methods for a Subclass of SDPs

- Computer Science
- 1999

This paper develops interior point methods for solving a subclass of the transformable linear SDP problems where the diagonal of a matrix variable is given and global convergence of these methods is proved. Expand