Related papers: Optimal breakpoint selection method for piecewise …

This paper presents a distributed resource allocation algorithm to jointly optimize the power allocation, channel allocation and relay selection for decode-and-forward (DF) relay networks with a large number of sources, relays, and…

The rotation averaging problem is a fundamental task in computer vision applications. It is generally very difficult to solve due to the nonconvex rotation constraints. While a sufficient optimality condition is available in the literature,…

This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…

In intensity-modulated radiation therapy, optimal intensity distributions of incoming beams are decomposed into linear combinations of leaf openings of a multileaf collimator (segments). In order to avoid inefficient dose delivery, the…

We study the optimization version of the set partition problem (where the difference between the partition sums are minimized), which has numerous applications in decision theory literature. While the set partitioning problem is NP-hard and…

This work proposes a general learned proximal alternating minimization algorithm, LPAM, for solving learnable two-block nonsmooth and nonconvex optimization problems. We tackle the nonsmoothness by an appropriate smoothing technique with…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

We propose a simple subsampling scheme for fast randomized approximate computation of optimal transport distances. This scheme operates on a random subset of the full data and can use any exact algorithm as a black-box back-end, including…

This paper deals with nonconvex stochastic optimization problems in deep learning and provides appropriate learning rates with which adaptive learning rate optimization algorithms, such as Adam and AMSGrad, can approximate a stationary…

Controlling complex tasks in robotic systems, such as circular motion for cleaning or following curvy lines, can be dealt with using nonlinear vector fields. In this paper, we introduce a novel approach called rotational obstacle avoidance…

Probabilistic sampling-based algorithms, such as the probabilistic roadmap (PRM) and the rapidly-exploring random tree (RRT) algorithms, represent one of the most successful approaches to robotic motion planning, due to their strong…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…

Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of…

Adaptive regularized framework using cubics has emerged as an alternative to line-search and trust-region algorithms for smooth nonconvex optimization, with an optimal complexity amongst second-order methods. In this paper, we propose and…

Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min-max) problem over the so-called trial…

We study two-stage stochastic optimization problems with random recourse, where the adaptive decisions are multiplied with the uncertain parameters in both the objective function and the constraints. To mitigate the computational…

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one…

Network adaptation is essential for the efficient operation of Cloud-RANs. Unfortunately, it leads to highly intractable mixed-integer nonlinear programming problems. Existing solutions typically rely on convex relaxation, which yield…

The optimal control input for linear systems can be solved from algebraic Riccati equation (ARE), from which it remains questionable to get the form of the exact solution. In engineering, the acceptable numerical solutions of ARE can be…