Related papers: Optimal Solution of Nonlinear Fuzzy Optimization P…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…
We introduce the concept of strong high-order approximate minimizers for nonconvex optimization problems. These apply in both standard smooth and composite non-smooth settings, and additionally allow convex or inexpensive constraints. An…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
Optimal transport problems pose many challenges when considering their numerical treatment. We investigate the solution of a PDE-constrained optimisation problem subject to a particular transport equation arising from the modelling of image…
In this paper, we present some new necessary and sufficient optimality conditions in terms of the Clarke subdifferentials for approximate Pareto solutions of a nonsmooth vector optimization problem which has an infinite number of…
We study the optimal approximation of the solution of an operator equation Au=f by linear and nonlinear mappings. We identify those cases where optimal nonlinear approximation is better than optimal linear approximation.
To every nearly convex optimization problem, that is a minimization problem with a nearly convex objective function and a nearly convex constraint set, we associate a uniquely defined convex optimization problem with a lower semicontinuous…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
A new fuzzy optimization framework that extends FCM causality is proposed. This model utilizes the dynamics to map data into metrics and create a framework that examines logical implication and hierarchy of concepts using a multiplex.…
Modern optimisation algorithms are often metaheuristic, and they are very promising in solving NP-hard optimization problems. In this paper, we show how to use the recently developed Firefly Algorithm to solve nonlinear design problems. For…
In this paper, an optimization model with a linear objective function subjected to a system of fuzzy relation equations (FRE) is studied where the feasible region is defined by the Dombi t-norm. Dombi family of t-norms includes a parametric…
In the present paper, several types of efficiency conditions are established for vector optimization problems with cone constraints affected by uncertainty, but with no information of stochastic nature about the uncertain data. Following a…
This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous…
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations.…
In practice, most of the optimization problems are non-linear requiring certain interactive solutions and approaches to model. In 5G Advanced and Beyond network slicing, mathematically modeling the users, type of service distributions and…
This paper is a continuation of our work concerning the logical and computational foundations of multi-step fuzzy inference. We bring further results on the implementation of the Mamdani-Assilian type of fuzzy rules and inference in Goedel…
In this paper, we introduce maximum composition ordering problems. The input is $n$ real functions $f_1,\dots,f_n:\mathbb{R}\to\mathbb{R}$ and a constant $c\in\mathbb{R}$. We consider two settings: total and partial compositions. The…
Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…
We study filter based regularization methods for linear ill-posed problems between Hilbert spaces. We derive optimal order conditions under a-priori choice rules for the regularization parameter. Such analysis is applied to the fractional…