The Lebesgue property (order-continuity) of a monotone convex function on a solid vector space of measurable functions is characterized in terms of (1) the weak inf-compactness of the conjugate function on the order-continuous dual space, (2) the attainment of the supremum in the dual representation by order-continuous…
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48 results for “order continuous dual”
Paper explores closedness properties of convex sets in rearrangement invariant spaces.
problem Closedness properties of law-invariant convex sets in rearrangement invariant spaces.
method Analyzes equivalence of different closedness types in rearrangement invariant spaces.
result Order closedness, -closedness and -closedness of a law-invariant convex set are equivalent.
In the dual of a -Orlicz space , that we call a dual Orlicz space, we show that a proper (resp. finite) convex function is lower semicontinuous (resp. continuous) for the Mackey topology if and only if on each order interval (), it is lowe…
We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…
Researchers prove uniqueness and continuity of solution to L_p dual Minkowski problem.
problem Proving uniqueness and continuity of solution to L_p dual Minkowski problem.
method Established new Minkowski-type inequalities related to optimization problem.
result Uniqueness and continuity of solution for general convex bodies when .
The important application of semi-static hedging in financial markets naturally leads to the notion of quasi self-dual processes which is, for continuous semimartingales, related to symmetry properties of both their ordinary as well as their stochastic logarithms. We provide a structure result for continuous quasi self…
Dual representations for robust risk measures and uncertainty sets.
problem Characterizing continuity of robust risk measures and their uncertainty sets.
method Develop dual representations for robust risk measures and uncertainty sets based on distinct geometric assumptions.
result Two dual frameworks for consolidated uncertainty sets are complementary, not interchangeable.
In this paper we continue our study of the fourth order transgression on hyperähler manifolds introduced in the previous paper. We give a local construction for the fourth-order transgression of the Chern character form of an arbitrary vector bundle supplied with a self-dual connection on a four dimensional hyperkähler…
In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian) an explicit second-order expansion formula for the power investor's value function - seen as a function of the underlying market price of risk process - is provided. T…
A Primal Dual Active Set with Continuation Algorithm for the \ell^0-Regularized Optimization Problemmath.OC
We develop a primal dual active set with continuation algorithm for solving the \ell^0-regularized least-squares problem that frequently arises in compressed sensing. The algorithm couples the the primal dual active set method with a continuation strategy on the regularization parameter. At each inner iteration, it fir…
We present a construction of complete self-dual Einstein metrics of negative scalar curvature on an uncountable family of manifolds of infinite topological type, which are enumerated by continued fraction expansions of irrational numbers. These manifolds may be regarded as limits of the resolutions of cyclic quotient s…
We consider empirical risk minimization of linear predictors with convex loss functions. Such problems can be reformulated as convex-concave saddle point problems, and thus are well suitable for primal-dual first-order algorithms. However, primal-dual algorithms often require explicit strongly convex regularization in …
New algorithm approximates continuous Wasserstein barycenters efficiently.
problem Computing Wasserstein barycenters for continuous distributions.
method Stochastic algorithm using dual potentials and stochastic gradient descent.
result Efficient online approximation of continuous Wasserstein barycenters.
A new method for faster optimization on statistical manifolds.
problem Slow convergence of first-order methods in manifold optimization.
method Dual Riemannian Newton method on manifolds with dual connections.
result Local quadratic convergence of the dual Riemannian Newton method.
Continuous-time mean-variance portfolio selection model with nonlinear wealth equations and bankruptcy prohibition is investigated by the dual method. A necessary and sufficient condition which the optimal terminal wealth satisfies is obtained through a terminal perturbation technique. It is also shown that the optimal…
In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …
New methods solve MI problems with locally Lipschitz operators, improving solution efficiency.
problem Solving monotone inclusions with locally Lipschitz continuous operators.
method Primal-dual extrapolation methods using backtracking line search.
result Improved operation complexity for solving MI problems.
Avanzi et al. (2016) recently studied an optimal dividend problem where dividends are paid both periodically and continuously with different transaction costs. In the Brownian model with Poissonian periodic dividend payment opportunities, they showed that the optimal strategy is either of the pure-continuous, pure-peri…
Researchers compute Wodzicki residue for pseudo-differential operators on compact Lie groups.
problem Computing the Wodzicki residue for pseudo-differential operators on compact Lie groups.
method Analytic continuation of traces and matrix-valued symbols.
result Main theorem complementary to [2], removing ellipticity hypothesis.
Extends martingale Schrödinger bridge to arbitrary dimensions and characterizes it.
problem Tackles the martingale Schrödinger bridge in arbitrary dimensions.
method Identifies continuous-time counterpart and relates to variational problems.
result Continuous martingale Schrödinger bridge coincides with Föllmer martingale in irreducible case.
In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise differential inclusion. In the …
Characterizes continuity of monotone functionals in mixed topology.
problem Continuity of monotone functionals in mixed topology.
method Characterization through lower semicontinuity and dual representations.
result Continuity in mixed topology is equivalent to dual representation in terms of countably additive measures.
On dual-projectively equivalent connections associated to second order superintegrable systemsmath.DG
New connections share geodesics with superintegrable systems.
problem Understanding geodesics in affine connections related to superintegrable systems.
method Analyzing dual-geodesics and comparing them across different connections.
result Certain torsion-free affine connections associated with second order superintegrable systems share the same dual-geodesics.
The dual problem of optimal transportation in Lorentz-Finsler geometry is studied. It is shown that in general no solution exists even in the presence of an optimal coupling. Under natural assumptions dual solutions are established. It is further shown that the existence of a dual solution implies that the optimal tran…
Shuffling the Stochastic Mirror Descent via Dual Lipschitz Continuity and Kernel Conditioningmath.OC
New method improves optimization algorithms without Lipschitz smoothness.
problem Improving optimization algorithms in the absence of Lipschitz smoothness.
method Dual kernel conditioning (DKC) to provide dual Lipschitz continuity.
result First complexity bounds and iterate convergence for random reshuffling mirror descent.
A method to improve sequential learning by keeping past data errors in check.
problem Challenges in sequential learning with Gaussian processes due to accumulating errors.
method Memory-based dual sparse variational Gaussian processes.
result Improves accuracy in inference and learning for various applications.
Paper tackles class-incremental time series classification with dual-stream feature extraction.
problem Class-incremental continual learning for multivariate time series data.
method Dual-stream feature extraction pipeline combining deep temporal embedding features and statistical features.
result Competitive average accuracy across multiple datasets with low forgetting rates.
New method trains normalizing flows using entropy-regularized transport.
problem Training continuous normalizing flows efficiently.
method Formulates flows as gradients of scalar potentials, training only these potentials.
result Trains normalizing flows without explicit flow computation during training.
Unified Probabilistic Deep Continual Learning through Generative Replay and Open Set Recognitioncs.LG
Unified approach to continual learning using generative replay and open set recognition.
problem Catastrophic interference and recognition of out-of-distribution data in deep neural networks.
method Probabilistic approach based on variational inference in a deep autoencoder model, using generative replay and open set recognition.
result The approach significantly alleviates catastrophic interference and distinguishes out-of-distribution data.
The book can be divided in three parts: the Lagrange geometry of order , presented in the first three chapters, the geometrical theory of the dual manifolds - chapters 4-7 and the geometry of Hamilton spaces of order and their subspaces, contained in the last four chapters. They are studied directly an…
In this paper, we propose a new primal-dual algorithm for minimizing , where , , and are proper lower semi-continuous convex functions, is differentiable with a Lipschitz continuous gradient, and is a bounded linear operator. The proposed algorithm has some famous primal-dual algo…
This paper discusses the numéraire-based utility maximization problem in markets with proportional transaction costs. In particular, the investor is required to liquidate all her position in stock at the terminal time. We first observe the stability of the primal and dual value functions as well as the convergence of t…
All anti-self-dual Einstein metrics with non-zero cosmological constant arise from a single second-order PDE.
problem Anti-self-dual Einstein metrics with non-zero cosmological constant
method A second-order PDE introduced by Lipstein and Nagy
result All such metrics arise from this equation
Algorithm for exact partitioning of high-order models using convex tensor relaxation.
problem Exact partitioning of high-order models.
method Defining a general class of -degree Homogeneous Polynomial Models, relaxing the high-order combinatorial problem to a convex conic form problem, defining the Carathéodory symmetric tensor cone, and constructing a primal-dual certificate.
result The solution of the convex relaxation is correct and provides a statistical upper bound for exact partitioning.
The risk of financial positions is measured by the minimum amount of capital to raise and invest in eligible portfolios of traded assets in order to meet a prescribed acceptability constraint. We investigate nondegeneracy, finiteness and continuity properties of these risk measures with respect to multiple eligible ass…
This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is established. Consequently the optimal strategy of the consumption and investment proble…
Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable real-valued functions on n-dimensional Euclidean space. This generalizes intrinsic vol…
The study explores continuous noncrossing partitions and their relation to weighted circular factorizations.
problem Understanding the structure of continuous noncrossing partitions on the unit circle.
method Analyzes degree-d continuous noncrossing partitions and their equivalence classes of weighted linear factorizations.
result Maximal elements in the poset of continuous noncrossing partitions form a subspace homeomorphic to the dual Garside classifying space for the d-strand braid group.
New method accelerates convergence for entropy-regularized reinforcement learning problems.
problem Slow convergence of standard first-order methods for entropy-regularized Markov decision processes.
method Introduce a quadratically convexified primal-dual formulation and a new interpolating metric to accelerate convergence.
result Global convergence and exponential convergence rate for the new method.
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit …
New method for practical hedging under uncertainty in continuous time models.
problem High minimal superhedging price for practical use in continuous-time models.
method Relaxed hedging criterion based on acceptable shortfall risks, combining aggregation and convex dual representation theorems.
result Derivation of duality results for minimal price on discounted claims.
Improved first-order algorithm for entropy regularized OT with faster convergence.
problem Solving entropy regularized optimal transport efficiently.
method Accelerated primal-dual stochastic mirror descent algorithm with variance reduction.
result Improved rate from to .
The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networksstat.ML
Dual PC algorithm improves structure learning of Bayesian networks.
problem Learning the structure of Bayesian networks from observational data.
method Dual PC algorithm, leveraging covariance and precision matrices, and partial correlations.
result The dual PC algorithm outperforms the classic PC algorithm in structure recovery, even with non-Gaussian data.
The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided. This abstract generalization is set in a Banach lattice with a order unit. The primal problem is given as the supremum o…
Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
problem Nonconvex minimax problems with coupled linear constraints.
method Zeroth-order primal-dual alternating projected gradient (ZO-PDAPG) and zeroth-order regularized momentum primal-dual projected gradient (ZO-RMPDPG) algorithms.
result Iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints.
Study generalizes Yang-Mills equations for special complex surfaces.
problem Deriving equations for self-dual Yang-Mills fields on complex surfaces.
method Generalization of flat space Yang's and Newman's equations to conformally Kahler Riemannian 4-manifolds.
result Continuous group of hidden symmetries found only for conformally half-flat geometry.
New framework for fair online allocation in continuous time with deadlines.
problem Fair allocation under deadlines in continuous-time online learning.
method Continuous-time utility maximization, dual ascent optimization for time averages.
result Achieves regret bound in the absence of statistical knowledge.
PAPAL algorithm finds mixed Nash equilibria in continuous games.
problem Finding mixed Nash equilibria in non-convex, non-concave games.
method Particle-based Primal-Dual Algorithm (PAPAL) for weakly entropy-regularized min-max optimization.
result PAPAL offers non-asymptotic convergence guarantees for -mixed Nash equilibrium.