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Optimization problems in disciplines such as machine learning are commonly solved with iterative methods. Gradient descent algorithms find local minima by moving along the direction of steepest descent while Newton's method takes into…
This paper initiates a systematic development of a theory of non-commutative optimization. It aims to unify and generalize a growing body of work from the past few years which developed and analyzed algorithms for natural geodesically…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
In this paper, we introduce a new method for compactification of a topological space by order topology and through ordinal numbers. The idea behind our approach originates from the definition of a limit point, and then we try to find an…
A common problem in the optimization of structures is the handling of uncertainties in the parameters. If the parameters appear in the constraints, the uncertainties can lead to an infinite number of constraints. Usually the constraints…
Alternating-Current Optimal Power Flow (AC-OPF) is framed as a NP-hard non-convex optimization problem that solves for the most economical dispatch of grid generation given the AC-network and device constraints. Although there are no…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…
The linear convex log-homotopy has been used in the derivation of particle flow filters. One natural question is whether it is beneficial to consider other forms of homotopy. We revisit this question by considering a general linear form of…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the…
The Promise Constraint Satisfaction Problem (PCSP for short) is a generalization of the well-studied Constraint Satisfaction Problem (CSP). The PCSP has its roots in such classic problems as the Approximate Graph Coloring and the…
The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries…
Many machine learning models involve solving optimization problems. Thus, it is important to deal with a large-scale optimization problem in big data applications. Recently, subsampled Newton methods have emerged to attract much attention…
This paper proposes novel algorithm for non-convex multimodal constrained optimisation problems. It is based on sequential solving restrictions of problem to sections of feasible set by random subspaces (in general, manifolds) of low…
A numerical method for coupled 3D-1D problems with discontinuous solutions at the interfaces is derived and discussed. This extends a previous work on the subject where only continuous solutions were considered. Thanks to properly defined…
The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…
This paper presents a computationally efficient optimization algorithm for solving nonconvex optimal control problems that involve discrete logic constraints. Traditional solution methods for these constraints require binary variables and…
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…
Classical gradient-based density topology optimization is adapted for method-of-moments numerical modeling to design a conductor-based system attaining the minimal antenna Q-factor evaluated via an energy stored operator. Standard topology…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…