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Jacobian Schemes of Conic-Line Arrangements and Eigenschemes
The Jacobian scheme of a reduced, singular projective plane curve is the zero-dimensional scheme, whose homogeneous ideal is generated by the...
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Conic Nonholonomic Constraints on Surfaces and Control Systems
This paper addresses the equivalence problem of conic submanifolds in the tangent bundle of a smooth 2-dimensional manifold. Those are given by a...
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Conic sections
Intersections of a right circular conical surface Σ with a plane ε, orthogonal to its axis and not passing through its apex O, are circles...
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Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming
Conic linear programs in locally convex Hausdorff topological vector spaces are addressed in this paper. Solution existence for the dual problem, as...
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Closed-Form Solution of Conic in Point-Line Enumerative Problem of Conic
We use the reciprocal transformation to propose the closed-form solutions to the conics through m points and tangent to n lines satisfying
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Disjunctive cuts in Mixed-Integer Conic Optimization
This paper studies disjunctive cutting planes in Mixed-Integer Conic Programming. Building on conic duality, we formulate a cut-generating conic...
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Applications of Conic Programming in Non-smooth Mechanics
In the field of nonlinear mechanics, many challenging problems (e.g., plasticity, contact, masonry structures, nonlinear membranes) turn out to be...
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Conic Sections
The conic sectionsconic section got their name from the fact that they can be generated as the intersection of a straight cone with a plane...
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Hessian barrier algorithms for non-convex conic optimization
A key problem in mathematical imaging, signal processing and computational statistics is the minimization of non-convex objective functions that may...
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Performance enhancements for a generic conic interior point algorithm
In recent work, we provide computational arguments for expanding the class of proper cones recognized by conic optimization solvers, to permit...
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Sparse conic reformulation of structured QCQPs based on copositive optimization with applications in stochastic optimization
Recently, Bomze et al. introduced a sparse conic relaxation of the scenario problem of a two stage stochastic version of the standard quadratic...
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Conic-Line Arrangements in the Complex Projective Plane
The main goal of this note is to begin a systematic study on conic-line arrangements in the complex projective plane. We show a de Bruijn–Erdős type...
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Remarks on asymptotic isometric embeddings of conic transforms for torus actions
Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given...
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Mixed-integer exponential conic optimization for reliability enhancement of power distribution systems
This paper develops an optimization model for determining the placement of switches, tie lines, and underground cables in order to enhance the...
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Conic Relaxations with Stable Exactness Conditions for Parametric Robust Convex Polynomial Problems
In this paper, we examine stable exact relaxations for classes of parametric robust convex polynomial optimization problems under affinely...
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Conic formulation of QPCCs applied to truly sparse QPs
We study (nonconvex) quadratic optimization problems with complementarity constraints, establishing an exact completely positive reformulation...
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On the nearly freeness of conic-line arrangements with nodes, tacnodes, and ordinary triple points
In the present note, we provide a partial classification of nearly free conic-line arrangements in the complex plane having nodes, tacnodes, and...
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Geometric Properties of Blaschke-Like Maps on Domains with a Conic Boundary
For a circle C contained in the unit disk, the necessary and sufficient condition for the existence of a triangle inscribed in the unit circle and...
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Real-Fibered Morphisms of del Pezzo Surfaces and Conic Bundles
It goes back to Ahlfors that a real algebraic curve admits a real-fibered morphism to the projective line if and only if the real part of the curve...
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Axially Symmetric Vibration of a Complete Conic Shell
We develop a variational method for the solution of the spectral problem of free axially symmetric vibration of a thin-walled conic shell with...