Related papers: Oracle Tractability of Skew Bisubmodular Functions
In this paper, we introduce a subclass of close-to-convex functions defined in the open unit disk. We obtain the inclusion relationships, coefficient estimates and Fekete-Szego inequality. The results presented here would provide extension…
In this paper we extend the Shepard-Bernoulli operators introduced in [6] to the bivariate case. These new interpolation operators are realized by using local support basis functions introduced in [23] instead of classical Shepard basis…
In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined…
In a seminal paper, Choquet introduced an integral formula to extend a monotone increasing setfunction on a sigma-algebra to a (nonlinear) functional on bounded measurable functions. The most important special case is when the setfunction…
In this paper, we use various versions of Lov\'asz extension to systematically derive continuous formulations of problems from discrete mathematics. This will take place in the following context: (1) For combinatorial optimization problems…
The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex optimization over spaces of tensors is now gaining much interest…
The problem of maximizing non-negative monotone submodular functions under a certain constraint has been intensively studied in the last decade. In this paper, we address the problem for functions defined over the integer lattice. Suppose…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
It is known that a subharmonic function of finite order $\rho$ can be approximated by the logarithm of the modulus of an entire function at the point $z$ outside an exceptional set up to $C\log|z|$. In this article we prove that if such an…
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and…
We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order…
In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…
This paper considers submodular function minimization (SFM) restricted to a family of subsets. We show that SFM over complements of families with certain hierarchical structures can be solved in polynomial-time. This yields a…
In this paper, we consider the class of quasiconvex functions and its proper subclass of conic functions. The integer minimization problem of these functions is considered in the paper, assuming that an optimized function is defined by the…
Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…
The symmetric decreasing rearrangement of functions on $\mathbb{R}^n$ features in several seminal inequalities, such as the P\'olya-Szeg\H{o} inequality. The latter was shown by the authors to hold for all smoothing rearrangements, a class…
In this paper, we develop topological modules over the ring of bicomplex numbers. We discuss bicomplex convexivity, hyperbolic-valued seminorms and hyperbolic-valued Minkowski functionals in bicomplex modules. We also study the conditions…
Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…
We consider the problem of minimizing a function that is a sum of convex agent functions plus a convex common public function that couples them. The agent functions can only be accessed via a subgradient oracle; the public function is…
Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have…