Related papers: Classical linear vector optimization duality revis…
In this paper we provide some new sufficient conditions that ensure the existence of the solution of a weak vector equilibrium problem in Hausdorff topological vector spaces ordered by a cone. Further, we introduce a dual problem and we…
Consider a polyhedral convex cone which is given by a finite number of linear inequalities. We investigate the problem to project this cone into a subspace and show that this problem is closely related to linear vector optimization: We…
In this paper, we are dealing with constrained vector optimisation problems where the objective function acts between real linear-topological spaces. Our aim is to study the relationships between the sets of properly efficient solutions to…
We study geometric duality for convex vector optimization problems. For a primal problem with a $q$-dimensional objective space, we formulate a dual problem with a $(q+1)$-dimensional objective space. Consequently, different from an…
Recently wide application in engineering-economic problems was received with problems of vector optimization. Development of methods of the decision of these problems it is executed in works A. Messac and others. Complexity of the offered…
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,…
Geometric duality theory for multiple objective linear programming problems turned out to be very useful for the development of efficient algorithms to generate or approximate the whole set of nondominated points in the outcome space. This…
We provide three new proofs of the strong concavity of the dual function of some convex optimization problems. For problems with nonlinear constraints, we show that the the assumption of strong convexity of the objective cannot be weakened…
Recently, Yamanaka and Yamashita proposed the so-called positively homogeneous optimization problem, which includes many important problems, such as the absolute-value and the gauge optimizations. They presented a closed form of the dual…
Langrange duality theorems for vector and set optimization problems which are based on an consequent usage of infimum and supremum (in the sense greatest lower and least upper bounds with respect to a partial ordering) have been recently…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
In this article we dwell into the class of so called ill posed Linear Inverse Problems (LIP) in machine learning, which has become almost a classic in recent times. The fundamental task in an LIP is to recover the entire signal / data from…
In this paper we provide sufficient conditions that ensure the existence of the solution of some vector equilibrium problems in Hausdorff topological vector spaces ordered by a cone. The conditions that we consider are imposed not on the…
We show that a broad range of convex optimization algorithms, including alternating projection, operator splitting, and multiplier methods, can be systematically derived from the framework of subspace correction methods via convex duality.…
This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality…
We consider an optimization problem with positively homogeneous functions in its objective and constraint functions. Examples of such positively homogeneous functions include the absolute value function and the $p$-norm function, where $p$…
Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and…