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In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path…
We develop a new interior-point method (IPM) for symmetric-cone optimization, a common generalization of linear, second-order-cone, and semidefinite programming. In contrast to classical IPMs, we update iterates with a geodesic of the cone…
In this paper, we propose a new optimization method for independent low-rank matrix analysis (ILRMA) based on a parametric majorization-equalization algorithm. ILRMA is an efficient blind source separation technique that simultaneously…
We describe an iterative method to optimize the multi-scale entanglement renormalization ansatz (MERA) for the low-energy subspace of local Hamiltonians on a D-dimensional lattice. For translation invariant systems the cost of this…
The robust truss topology optimization against the uncertain static external load can be formulated as mixed-integer semidefinite programming. Although a global optimal solution can be computed with a branch-and-bound method, it is very…
The multi-scale entanglement renormalization ansatz (MERA) is a hierarchical class of tensor network states motivated by the real-space renormalization group. It is used to simulate strongly correlated quantum many-body systems. For…
Iterative image reconstruction (IIR) algorithms in Computed Tomography (CT) are based on algorithms for solving a particular optimization problem. Design of the IIR algorithm, therefore, is aided by knowledge of the solution to the…
In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from…
An implicit mass-matrix penalization (IMMP) of Hamiltonian dynamics is proposed, and associated dynamical integrators, as well as sampling Monte-Carlo schemes, are analyzed for systems with multiple time scales. The penalization is based on…
Analytic and optimization methods for solving inverse kinematics (IK) problems have been deeply studied throughout the history of robotics. The two strategies have complementary strengths and weaknesses, but developing a unified approach to…
Indexed modulation (IM) is an evolving technique that has become popular due to its ability of parallel data communication over distinct combinations of transmission entities. In this article, we first provide a comprehensive survey of…
In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set…
Low-rank adaptations (LoRA) are widely used to fine-tune large models across various domains for specific downstream tasks. While task-specific LoRAs are often available, concerns about data privacy and intellectual property can restrict…
Optimization tasks are crucial in statistical machine learning. Recently, there has been great interest in leveraging tools from dynamical systems to derive accelerated and robust optimization methods via suitable discretizations of…
The integration of Large Language Models (LLMs) into optimization has created a powerful synergy, opening exciting research opportunities. This paper investigates how LLMs can enhance existing optimization algorithms. Using their…
In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…
We present an algorithm to compute planar linkage topology and geometry, given a user-specified end-effector trajectory. Planar linkage structures convert rotational or prismatic motions of a single actuator into an arbitrarily complex…
This draft concerns the error analysis of a collocation method based on the moving least squares (MLS) approximation for integral equations, which improves the results of [2] in the analysis part. This is mainly a translation from Persian…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…