Related papers: Designing Gabor windows using convex optimization
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
When faced with multiple minima of an "inner-level" convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary "outer-level" convex objective of interest. Bilevel…
Gabor frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. Finding general and verifiable conditions which imply…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
We study the duality of reconstruction systems, which are $g$-frames in a finite dimensional setting. These systems allow redundant linear encoding-decoding schemes implemented by the so-called dual reconstruction systems. We are…
We show that $(g_2,a,b)$ is a Gabor frame when $a>0, b>0, ab<1$ and $g_2(t)=({1/2}\pi \gamma)^{{1/2}} (\cosh \pi \gamma t)^{-1}$ is a hyperbolic secant with scaling parameter $\gamma >0$. This is accomplished by expressing the Zak transform…
Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…
Motivated by an inertial primal-dual dynamical system with vanishing damping, we propose a class of accelerated augmented Lagrangian methods with Nesterov extrapolation parameters for a linearly constrained convex optimization problem with…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
In this paper, we study multiwindow discrete Gabor $(M-D-G)$ systems $\mathcal{G}(g,L,M,N)$ on discrete periodic sets $\mathbb{S}$ and give some necessary and/or sufficient matrix-conditions for a $M-D-G$ system in $\ell^2(\mathbb{S})$ to…
A computationally-fast inverse design method for nanophotonic structures is presented. The method is based on two complementary convex optimization problems which modify the dielectric structure and resonant field respectively. The design…
We investigate an alternative solution method to the joint signal-beamformer optimization problem considered by Setlur and Rangaswamy[1]. First, we directly demonstrate that the problem, which minimizes the received noise, interference, and…
We consider a general multi-agent convex optimization problem where the agents are to collectively minimize a global objective function subject to a global inequality constraint, a global equality constraint, and a global constraint set.…
Various applications in signal processing and machine learning give rise to highly structured spectral optimization problems characterized by low-rank solutions. Two important examples that motivate this work are optimization problems from…
In recent times the Douglas-Rachford algorithm has been observed empirically to solve a variety of nonconvex feasibility problems including those of a combinatorial nature. For many of these problems current theory is not sufficient to…
Optimizing an implicational base of a closure system consists in turning this implicational base into an equivalent one with premises and conclusions as small as possible. This task is known to be hard in general but tractable for a number…
Douglas-Rachford splitting and the alternating direction method of multipliers (ADMM) can be used to solve convex optimization problems that consist of a sum of two functions. Convergence rate estimates for these algorithms have received…