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Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules
In this paper we introduce a new parameterized Quadratic Decision Rule (QDR), a generalisation of the commonly employed Affine Decision Rule (ADR),...
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On the Structure of Pointsets with Many Collinear Triples
It is conjectured that if a finite set of points in the plane contains many collinear triples, then part of the set has a structure. We will show...
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Cheeger–Colding–Tian Theory for Conic Kähler–Einstein Metrics
In this paper we extend the Cheeger–Colding–Tian theory to the conic Kahler–Einstein metrics. In general, there are no smooth approximations of a...
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Minimization of Even Conic Functions on the Two-Dimensional Integral Lattice
Under consideration is the Successive Minima Problem for the 2-dimensional lattice with respect to the order given by some conic function f . We...
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Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
In this paper, we study divisorial ideals of a Hibi ring which is a toric ring arising from a partially ordered set. We especially characterize the...
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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming
Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built...
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Copositive Matrices, Sums of Squares and the Stability Number of a Graph
This chapter investigates the cone of copositive matrices, with a focus on the design and analysis of conic inner approximations for it. These...
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Brianchon and Poncelet’s joint memoir, the nine-point circle, and beyond
In this paper, we give a thorough account of Brianchon and Poncelet’s joint memoir on equilateral hyperbolas subject to four given conditions,...
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Variational Analysis of Norm Cones in Finite Dimensional Euclidean Spaces
A norm cone in a finite dimensional Euclidean space is the epigraph of a norm. Many important practical optimization problems are formulated as norm...
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Conic Sections in Early Modern Europe. Second Part: Philippe de la Hire on Conics
After the preliminary work on circles, La Hire moved to the conic sections. He defined them as had Apollonius: the section of a conic surface by a...
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Amplified endomorphisms of Fano fourfolds
Let X be a smooth Fano fourfold admitting a conic bundle structure. We show that X is toric if and only if X admits an amplified endomorphism; in...
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Construction of Free Curves by Adding Lines to a Given Curve
In the present note we construct new families of free plane curves starting from a curve C and adding high order inflectional tangent lines of C ,...
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Data-Driven Distributionally Robust Risk-Averse Two-Stage Stochastic Linear Programming over Wasserstein Ball
In this paper, we consider a data-driven distributionally robust two-stage stochastic linear optimization problem over 1-Wasserstein ball centered at...
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The Nonconvex Second-Order Cone: Algebraic Structure Toward Optimization
This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as...
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Grassmann Angles and Absorption Probabilities of Gaussian Convex Hulls
Let M be an arbitrary subset in ℝ n with a conic (or positive) hull C . Consider its Gaussian image AM , where A is a k × n -matrix whose entries are...
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Supermodularity and valid inequalities for quadratic optimization with indicators
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous...
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Solution refinement at regular points of conic problems
Many numerical methods for conic problems use the homogenous primal–dual embedding, which yields a primal–dual solution or a certificate establishing...
