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On a generalized Batyrev’s cone conjecture
We discuss some variants of cone theorem for movable curves in any codimension.
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A Relative Silting Theorem
Silting theorem gives a generalization of the classical tilting theorem of Brenner and Butler for a 2-term silting complex. In this paper, we give a...
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Second-order Optimality Conditions for Mathematical Program with Semidefinite Cone Complementarity Constraints and Applications
This paper is concerned with second-order optimality conditions for the mathematical program with semidefinite cone complementarity constraints. To...
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Relative Ding and K-stability of toric Fano manifolds in low dimensions
The purpose of this article is to clarify all of the uniformly relatively Ding stable toric Fano threefolds and fourfolds as well as unstable ones....
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Augmented Lagrangian cone method for multiobjective optimization problems with an application to an optimal control problem
This paper proposes an augmented Lagrangian method to compute Pareto optimal sets of multiobjective optimization problems. The method neither...
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Convex Separation and Some Consequences
This chapter mainly concerns convex separation theorems that play a fundamental role in convex analysis and its numerous applications. We also study...
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Bad projections of the PSD cone
The image of the cone of positive semidefinite matrices under a linear map is a convex cone. Pataki characterized the set of linear maps for which...
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Total positive curvature and the equality case in the relative isoperimetric inequality outside convex domains
We settle the case of equality for the relative isoperimetric inequality outside any arbitrary convex set with not empty interior.
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Refined operator inequalities for relative operator entropies
We investigate the relative operator entropies in the more general settings of C *-algebras, real C *-algebras and JC-algebras. We show that all the...
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A Donaldson–Uhlenbeck–Yau theorem for normal varieties and semistable bundles on degenerating families
In this paper, we first prove a Donaldson–Uhlenbeck–Yau theorem over projective normal varieties smooth in codimension two. As a consequence we...
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Lipschitz-like property relative to a set and the generalized Mordukhovich criterion
In this paper we will establish some necessary condition and sufficient condition respectively for a set-valued map** to have the Lipschitz-like...
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Łoskot-Rudnicki’s Inequality and General Relative Entropy Inequality for Cauchy Problems Preserving Positivity
The Generalized Relative Entropy inequality is a ubiquitous property in mathematical models applied in physics or biology. In spite of its...
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On approximations of the PSD cone by a polynomial number of smaller-sized PSD cones
We study the problem of approximating the cone of positive semidefinite (PSD) matrices with a cone that can be described by smaller-sized PSD...
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Augmented Lagrangian method for second-order cone programs under second-order sufficiency
This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the...
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Metric Regularity Relative to a Cone
The purpose of this paper is to discuss some of the highlights of the theory of metric regularity relative to a cone. For example, we establish a...
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Families of faces and the normal cycle of a convex semi-algebraic set
We study families of faces for convex semi-algebraic sets via the normal cycle which is a semi-algebraic set similar to the conormal variety in...
