## 11 Citations

Robust Linear Semi-infinite Optimization

- Computer Science
- 2014

The robust counterpart of an uncertain LSIO problem seldom enjoys the strong assumptions which are necessary to apply reduction or feasible point methods.

Selected Applications of Linear Semi-Infinite Systems Theory

- Mathematics
- 2020

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space ℝ n $\mathbb {R}^{n}$ (i.e.,…

FACES FOR TWO-QUBIT SEPARABLE STATES AND THE CONVEX HULLS OF TRIGONOMETRIC MOMENT CURVES

- Mathematics
- 2013

We analyze the facial structures of the convex set consisting of all two-qubit separable states. One of the faces is a four-dimensional convex body generated by the trigonometric moment curve arising…

A characterization of dual quermassintegrals and the roots of dual Steiner polynomials

- MathematicsAdvances in Mathematics
- 2018

Preliminaries on Linear Semi-infinite Optimization

- Computer Science
- 2014

Ordinary (or finite) linear optimization, linear infinite optimization, and linear semi-infinite optimization (LO, LIO, and LSIO in short) deal with linear optimization problems, where the dimension…

Addendum to: "An algebraic proof of the fundamental theorem of algebra"

- Mathematics
- 2018

We prove the fundamental theorem of algebra (FTA on brief) by using linear algebra. The proof which arises from a new equivalent reformulation of FTA also works for any infinite field, having root…

Faces for two qubit separable states and the convex hulls of trigonometric moment curves

- Mathematics
- 2013

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Modeling Uncertain Linear Semi-infinite Optimization Problems

- Computer Science
- 2014

In most LSIO applications part of the data are uncertain as a consequence of error measurements or estimations, which is inherent to the data in fields as environmental engineering, telecommunications, finance, spectrometry, health care, statistics, machine learning, or data envelopment analysis.

## References

SHOWING 1-10 OF 15 REFERENCES

Global Optimization with Polynomials and the Problem of Moments

- MathematicsSIAM J. Optim.
- 2001

It is shown that the problem of finding the unconstrained global minimum of a real-valued polynomial p(x): R n to R, in a compact set K defined byPolynomial inequalities reduces to solving an (often finite) sequence of convex linear matrix inequality (LMI) problems.

Conjugacy for Closed Convex Sets

- Mathematics
- 2005

Even though the polarity is a well defined operation for arbitrary subsets in the Euclidean n-dimensional space, the related operation of conjugacy of faces appears defined in the literature…

Neighborly and cyclic polytopes

- Mathematics
- 1963

Introduction. Let S be a finite set of points in n-space. A pair of points p and q of S are called neighbors if the segment joining them is an edge of the convex polytope spanned by S. Some years ago…

Lectures on Polytopes

- Mathematics
- 1994

Based on a graduate course given at the Technische Universitat, Berlin, these lectures present a wealth of material on the modern theory of convex polytopes. The clear and straightforward…

DUALITY, HAAR PROGRAMS, AND FINITE SEQUENCE SPACES.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1962

Using Theorem 0 and the fact that H*(X, E*) may be written in terms of Lie algebra cohomology, Theorem 1 is completed using several spectral sequences in Lie algebra Cohomology.

An Introduction to Convex Polytopes

- Mathematics
- 1982

1 Convex Sets.- 1. The Affine Structure of ?d.- 2. Convex Sets.- 3. The Relative Interior of a Convex Set.- 4. Supporting Hyperplanes and Halfspaces.- 5. The Facial Structure of a Closed Convex Set.-…

Discrete probability distributions and moment problem: numerical aspects

- MathematicsAppl. Math. Comput.
- 2001

A theorem on cyclic polytopes

- Mathematics
- 1968

LetC(ν, d) represent a cyclic polytope withν vertices ind dimensions. A criterion is given for deciding whether a given subset of the vertices ofC(ν, d) is the set of vertices of some face ofC(ν, d).…

Linear Semi-Infinite Optimization

- Mathematics
- 1998

MODELLING. Modelling with the Primal Problem. Modelling with the Dual Problem. LINEAR SEMI-INFINITE SYSTEMS. Alternative Theorems. Consistency. Geometry. Stability. THEORY OF LINEAR SEMI-INFINITE…