Related papers: A Strong Duality Principle for Equivalence Couplin…
A unified model is addressed for general optimization problems in multi-scale complex systems. Based on necessary conditions and basic principles in physics, the canonical duality-triality theory is presented in a precise way to include…
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…
The notion of duality -- that a given physical system can have two different mathematical descriptions -- is a key idea in modern theoretical physics. Establishing a duality in lattice statistical mechanics models requires the construction…
We consider the minimization problem of $\phi$-divergences between a given probability measure $P$ and subsets $\Omega$ of the vector space $\mathcal{M}_\mathcal{F}$ of all signed finite measures which integrate a given class $\mathcal{F}$…
We present a strong-weak coupling duality for quantum mechanical potentials. Similarly to what happens in quantum field theory, it relates two problems with inverse couplings, leading to a mapping of the strong coupling regime into the weak…
In this paper a new look on the electro-magnetic duality is presented and appropriately exploited. The duality analysis in the nonrelativistic and relativistic formulations is shown to lead to the idea the mathematical model field to be a…
We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…
This article develops a duality principle applicable to a large class of variational problems. Firstly, we apply the results to a Ginzburg-Landau type model. In a second step, we develop another duality principle and related primal dual…
This article studies convex duality in stochastic optimization over finite discrete-time. The first part of the paper gives general conditions that yield explicit expressions for the dual objective in many applications in operations…
We start by describing two of the main proposals for duality in Abelian gauge theories, namely $F$(ield strength)-duality approach and the $S$% -duality formalism. We then discuss how $F$-duality and $S$-duality can be applied to the case…
We consider the Monge-Kantorovich transport problem in an abstract measure theoretic setting. Our main result states that duality holds if $c:X\times Y\to [0,\infty)$ is an arbitrary Borel measurable cost function on the product of Polish…
Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the…
We show that a wide class of risk-constrained nonconvex functional optimization problems exhibit strong duality, regardless of nonconvexity. We develop two novel results under distinct sets of assumptions, establishing strong duality over…
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,…
In this paper we associate with an infinite family of real extended functions defined on a locally convex space, a sum, called robust sum, which is always well-defined. We also associate with that family of functions a dual pair of problems…
In this paper we develop a duality theory for all finite-dimensional near-vector spaces and introduce a notion of inner product tailored to the broad and natural class of strongly regular near-vector spaces. This generalized construction…
Double field theory and exceptional field theory are formulations of supergravity that make certain dualities manifest symmetries of the action. To achieve this, the geometry is extended by including dual coordinates corresponding to…
We formulate the necessary and sufficient conditions for the existence of a pair of maximally incompatible two-outcome measurements in a finite dimensional General Probabilistic Theory. The conditions are on the geometry of the state space,…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
We perform an in-depth analysis of the transformation rules under duality for couplings of theories containing multiple scalars, $p$-form gauge fields, linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar reasoning to…