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Showing 1 to 20 of 34 for “"Convex functions"”.
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Optimal transportation and barycenter problems via convex functions
… transportation is approached by studying the convex functions underlying optimal transports, listing convex functions for known transports and introduce new cases. Chapter six develops barycentric applications. The rst section develops 2-Wasserstein barycenter results. Using a xed-point …
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Best Approximation With Geometric Constraints
… to a function in L<sub>p </sub>(0,1) by convex functions, (m, n)-convex functions, (m, n)-convex functions and (m, n)-convex splines, for 1 < p < ∞ , and best uniform approximation to a continuous function by convex functions, quasi-convex functions and piecewise monotone functions.</p>
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Optimization, Convergence, and Duality
… a notion of convergence for a sequence of convex functions was studied by Wijsman, Mosco, and Joly. This convergence, not comparable to pointwise convergence, has several important properties: it is preserved under the Fenchel transform, and it is equivalent to a convergence which can be …
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Convexity and curvature in Lorentzian geometry
… these curvature bound conditions together with convex functions are effective means to study the geometry of space-times. Chapter 3 explores the relation between convex functions and geodesic connectedness of space-times. We give geometric-topological proofs of geodesic connectedness for classes …
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Coordinating inventory control and pricing strategies
… case, we show, by employing the classical k-convexity concept, that a simple policy, called (s, S, p), is optimal when the demand functions are additive. For the model with more general demand functions, we show that an (s, S, p) policy is not necessarily optimal. We introduce a new concept, …
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M♮-convexity, S-convexity, and their applications in operations
… models maximizing submodular objective functions, and it is desirable to derive structural properties including monotone comparative statics of the optimal solutions or preservation of submodularity under the optimization operations. Yet, this task is challenging because the classical …
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Greed, hedging, and acceleration in convex optimization
… motivated problem of minimizing a strongly convex, smooth function with first-order information. The first main message of the thesis is that, surprisingly, algorithms which are individually suboptimal can be combined to achieve accelerated convergence rates. This phenomenon can be intuively …
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Fractional calculus operator and its applications to certain classes of analytic functions. A study on fractional derivative operator in analytic and multivalent functions.
… concerning analytic and -valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. …
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Asymptotic Behaviour and Derivation of Mean Field Models
… system for locating saddle points of concave-convex functions. This method is widely used in distributed optimisation over networks, for example in power systems and in rate control in communication networks. Chapter 3 gives an exact characterisation of the limiting solutions of the gradient …
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Generalized Matrix-fractional Functions and Their Applications
The support function of a closed convex set is a central object in convex geometry as it completely identifies the underlying set. For a particular class of sets -- the graph of matrix valued mapping $Y\mapsto -\half YY^T$ over an affine manifold $\set{Y\in\Rnm}{AY=B}$, their support functions are …
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Essays on Metric Spaces and Macro-Finance [védés előtt]
… with it’s important trigonometric angles, semi-convex functions, sequence of these functions and the associated gradient flows. Chapter 2. relies on the mathematical concepts and characteristics from Chapter 1. and incorporates these mentioned features into the Mosco convergence of CAT(1)-space. …
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Almost weak Asplund spaces
Continuous convex functions have long been known to be generically differentiable on Euclidean spaces. However, in 1968 Asplund decided to investigate and classify those Banach spaces that possess this Euclidean space property. Specifically, Asplund investigated those Banach spaces on which every …
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On cutting planes for mixed-integer nonlinear programming
… to model and solve problems involving nonlinear functions, continuous, and discrete variables. The state-of-the-art solvers of mixed-integer nonlinear programs (MINLPs) use a combination of, among other techniques, branch- and-bound and cutting planes. In the late ’90s, solvers for mixed-integer …
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Enhancing surveillance video captured in inclement weather
… is presented, which means good solutions to convex functions of label difference can now be found efficiently. More importantly, the multilabel swap algorithm provides a flexible trade-off (in terms of solution quality and efficiency) over the range of current multilabel graph-cut algorithms …
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Enhancing surveillance video captured in inclement weather
… is presented, which means good solutions to convex functions of label difference can now be found efficiently. More importantly, the multilabel swap algorithm provides a flexible trade-off (in terms of solution quality and efficiency) over the range of current multilabel graph-cut algorithms …
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Algorithms above the noise floor
… practice. Common examples include optimizing non-convex functions or optimizing over non-convex sets. In theory, such problems are usually NP-hard. But in practice, they are often solved sufficiently well for applications in machine learning and statistics. Even when a problem is convex, we often …
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Extremal functions related to convexity and martingales
… extremal function in the class of real-valued biconvex functions satisfying a boundary condition on a product of the unit ball with itself, with a suitable norm in the plane. We want to maximize the biconvex function at a point in the domain where the second component is fixed and therefore we …
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Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications
… dense data from real applications. Although the convex relaxations of these problems can be reformulated as either linear programming, second-order cone programming or semidefinite programming problems, the standard methods for solving these relaxations are not applicable because the problems are …
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