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We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality…
In this work, using a new geometrical approach we study to the existence of the fixed-point of mappings that independence of the smoothness, and also of their single-values or multi-values. This work proved the theorems that generalize in…
This paper mainly addresses the Monge mass transfer problem in the 1-D case. Through an ingenious approximation mechanism, one transforms the Monge problem into a sequence of minimization problems, which can be converted into a sequence of…
Generalized polyhedral convex optimization problems in locally convex Hausdorff topological vector spaces are studied systematically in this paper. We establish solution existence theorems, necessary and sufficient optimality conditions,…
This paper presents a canonical dual method for solving a quadratic discrete value selection problem subjected to inequality constraints. The problem is first transformed into a problem with quadratic objective and 0-1 integer variables.…
Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…
With this note we bring again into attention a vector dual problem neglected by the contributions who have recently announced the successful healing of the trouble encountered by the classical duals to the classical linear vector…
A problem of the erroneous duality gap caused by the presence of symmetries is solved in this paper utilizing point group theory. The optimization problems are first divided into two classes based on their predisposition to suffer from this…
Decentralized optimization is widely used in different fields of study such as distributed learning, signal processing, and various distributed control problems. In these types of problems, nodes of the network are connected to each other…
We shall firstly study the existence of one positive solution of a model problem for one equation via the classical Krasnosel'ski\u\i{} fixed-point theorem. Secondly we investigate how to handle this problem via the fixed point index theory…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and…
Most algorithms for solving optimization problems or finding saddle points of convex-concave functions are fixed-point algorithms. In this work we consider the generic problem of finding a fixed point of an average of operators, or an…
In recent years, there has been a surge of interest in studying different ways to reformulate nonconvex optimization problems, especially those that involve binary variables. This interest surge is due to advancements in computing…
The paper is dedicated to the study of strong duality for a problem of linear copositive programming. Based on the recently introduced concept of the set of normalized immobile indices, an extended dual problem is deduced. The dual problem…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…