# [PDF] Top 20 Convex Analysis for Minimizing and Learning Submodular Set Functions

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### Convex Analysis for Minimizing and Learning Submodular Set Functions

... synthetic **functions** that demonstrate this claim ...order **submodular** function by incorporating the constraints from Equation ...a **convex** recovery ...by **minimizing** the Fourier ` 1 norm, but vary ... See full document

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### Minimizing a sum of clipped convex functions

... (9) since the limit in (7) is equal to the limit in (8) unless x = 0. There are many **convex** **functions** that satisfy this superlinearity property. Some examples are the sum of squares function and the ... See full document

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### Minimizing Submodular Functions on Diamonds via Generalized Fractional Matroid Matchings

... consider **submodular** **functions** on the direct product of n diamonds U 1 , ...A **set** T ⊆ U is called a sub-transversal if |T ∩ U i | ≤ 1 for every i ∈ V ...the **set** of ... See full document

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### New performance guarantees for the greedy maximization of submodular set functions

... OF **SUBMODULAR** **SET** **FUNCTIONS** JUSSI LAITILA AND ATTE MOILANEN ...nondecreasing **submodular** **set** ...and **Convex** optimization and Greedy algorithm and Maximization and Steepest ... See full document

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### Minimizing Convex Piecewise-Affine Functions by Local Consistency Techniques

... the **set** of active subfunctions changes due to update of x, all the variables on which the activated or deactivated **functions** depend are again added to the ... See full document

122

### The e-support function of an e-convex set and conjugacy for e-convex functions

... e-**convex** **functions**. The classical support function of **Convex** **Analysis** is not appropriate for e-**convex** sets, since dif- ferent e-**convex** sets may have the same closure and ... See full document

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### Nesterov\u27s Smoothing Technique and Minimizing Differences of Convex Functions for Hierarchical Clustering

... Cluster **analysis** or clustering is one of the most important problems in many fields such as machine **learning**, pattern recognition, image **analysis**, data compression, and computer ...data **set** ... See full document

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### Difference of Convex Functions Programming for Reinforcement Learning

... Large Markov Decision Processes are usually solved using Approximate Dy- namic Programming methods such as Approximate Value Iteration or Ap- proximate Policy Iteration. The main contribution of this paper is to show ... See full document

10

### Iterative Regularization for Learning with Convex Loss Functions

... general **convex** loss **functions**. Within a statistical **learning** setting, we consider **convex** loss **functions** and propose a new form of iterative regularization based on the subgradient ... See full document

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### Minimizing Sparse High-Order Energies by Submodular Vertex-Cover

... In terms of optimization, these algorithms are designed to minimize objective **functions** (energies) containing unary and pairwise terms. Many inference problems must be modeled using high-order terms, not just ... See full document

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### Learning Set Functions with Limited Complementarity

... on **learning** of **set** func- tions, ...monotone **set** **functions** — complement-free **set** ...Such **set** **functions** model the natural property of diminishing returns, and are gener- ... See full document

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### Active-set Methods for Submodular Minimization Problems

... use alternating projection (Bauschke et al., 1997) and alternating reflection (Bauschke et al., 2004) algorithms to solve dual optimization problem in Eq. 20 . Nishihara et al. (2014) gave a extensive theoretical ... See full document

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### Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions

... performed **analysis** will be based on the second order characterization of pseudoconvexity given in [8] and it will give necessary and sufficient conditions for pseudoconvexity which are very easy to be ... See full document

14

### Convergence Analysis of a Proximal Point Algorithm for Minimizing Differences of Functions

... solving **convex** optimization problems and was extensively developed by Rockafellar [10] in the con- text of monotone variational ...for **minimizing** diﬀerences of **convex** **functions** have been ... See full document

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### Generalized convex set functions

... Properties and relations between these generalized convex set functions are investigated, and optimality criteria for differentiable and convex set functions are ext[r] ... See full document

13

### Analysis of Convex Functions

... of **convex** **functions** entails a powerful and elegant interaction be- tween **analysis** and ...Functional **Analysis** is the branch where people studies the extent to which the properties possessed by ... See full document

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### A Class of Submodular Functions for Document Summarization

... i P i = V and the P i s are disjoint) into separate clusters, and r i ≥ 0 indicates the singleton reward of i (i.e., the reward of adding i into the empty **set**). The value r i estimates the importance of i to the ... See full document

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### Maximization of Non-Monotone Submodular Functions

... Definition 61. (Secretary setting) Elements from Ω arrive one at a time, in a random sequence. The decision to accept or reject an item must be made before the subsequent item in the sequence arrives. The name ... See full document

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### Maximizing Bisubmodular and k-submodular Functions

... **Submodular** **functions** play a key role in combinatorial opti- mization and in the study of valued constraint satisfaction ...bisubmodular **functions**, which assign values to disjoint pairs of sets. Like ... See full document

14

### Convex functions

... Zagar, Susanna Maria, "**Convex** **functions**" (1996). Theses Digitization Project. 986. https://scholarworks.lib.csusb.edu/etd-project/986 This Thesis is brought to you for free and open access by the John M. ... See full document

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