Related papers: Iterated Linear Optimization
Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of…
In this paper, we introduce a new three-step iteration process in Banach space and prove convergence results for approximating fixed points for nonexpansive mappings. Also, we show that the newly introduced iteration process converges…
We investigate robust optimization problems defined for maximizing convex functions. For finite uncertainty set, we develop a geometric branch-and-bound algorithmic approach to solve this problem. The geometric branch-and-bound algorithm…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In…
We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that…
In this paper the local order of convergence used in iterative methods to solve nonlinear systems of equations is revisited, where shorter alternative analytic proofs of the order based on developments of multilineal functions are shown.…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
We consider an $\alpha$-relaxed projection $P_A^\alpha:H\to H$ given by $P_A^\alpha(x)=\alpha P_A(x)+(1-\alpha)x$ where $\alpha\in[0,1]$ and $P_A$ is the projection onto a non-empty, convex and closed subset $A$ of the real Hilbert space…
This article focuses on numerical efficiency of projection algorithms for solving linear optimization problems. The theoretical foundation for this approach is provided by the basic result that bounded finite dimensional linear optimization…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
Fixed points represent equilibrium states, stability, and solutions to a range of problems. It has been an active field of research. In this paper, we provide an overview of the main branches of fixed point theory. We discuss the key…
Many problems of theoretical and practical interest involve finding an optimum over a family of convex functions. For instance, finding the projection on the convex functions in $H^k(\Omega)$, and optimizing functionals arising from some…
We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
To optimize efficiently over discrete data and with only few available target observations is a challenge in Bayesian optimization. We propose a continuous relaxation of the objective function and show that inference and optimization can be…
The paper presents two edge grouping algorithms for finding a closed contour starting from a particular edge point and enclosing a fixation point. Both algorithms search a shortest simple cycle in \textit{an angularly ordered graph} derived…
Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations. This may cause…