On the characterizations of solutions to perturbed l1 conic optimization problem

Optimization ◽  
2019 ◽  
Vol 68 (6) ◽  
pp. 1157-1186
Author(s):  
Yong-Jin Liu ◽  
Ruonan Li ◽  
Bo Wang
Keyword(s):  
Optimization Problem ◽  
Conic Optimization

scholarly journals Separability of diagonal symmetric states: a quadratic conic optimization problem

Quantum ◽  
2018 ◽  
Vol 2 ◽  
pp. 45 ◽  
Author(s):  
Jordi Tura ◽  
Albert Aloy ◽  
Ruben Quesada ◽  
Maciej Lewenstein ◽  
Anna Sanpera
Keyword(s):  
Quantum Information ◽  
Optimization Problem ◽  
Entangled States ◽  
Conic Optimization ◽  
Entanglement Witnesses ◽  
Partial Transposition ◽  
Separability Problem ◽  
Necessary And Sufficient ◽  
Ppt Criterion ◽  
Symmetric States

We study the separability problem in mixtures of Dicke states i.e., the separability of the so-called Diagonal Symmetric (DS) states. First, we show that separability in the case of DS inCd⊗Cd(symmetric qudits) can be reformulated as a quadratic conic optimization problem. This connection allows us to exchange concepts and ideas between quantum information and this field of mathematics. For instance, copositive matrices can be understood as indecomposable entanglement witnesses for DS states. As a consequence, we show that positivity of the partial transposition (PPT) is sufficient and necessary for separability of DS states ford≤4. Furthermore, ford≥5, we provide analytic examples of PPT-entangled states. Second, we develop new sufficient separability conditions beyond the PPT criterion for bipartite DS states. Finally, we focus onN-partite DS qubits, where PPT is known to be necessary and sufficient for separability. In this case, we present a family of almost DS states that are PPT with respect to each partition but nevertheless entangled.

scholarly journals CQ-free optimality conditions and strong dual formulations for a special conic optimization problem

2020 ◽  
Vol 8 (3) ◽  
pp. 668-683
Author(s):  
Olga Kostyukova ◽  
Tatiana V. Tchemisova
Keyword(s):  
Optimality Conditions ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Constraint Qualifications ◽  
Strong Duality ◽  
Conic Optimization ◽  
First Order ◽  
Primal And Dual ◽  
Linear Cost ◽  
Strong Dual

In this paper, we consider a special class of conic optimization problems, consisting of set-semidefinite(or K-semidefinite) programming problems, where the set K is a polyhedral convex cone. For these problems, we introduce the concept of immobile indices and study the properties of the set of normalized immobile indices and the feasible set. This study provides the main result of the paper, which is to formulate and prove the new first-order optimality conditions in the form of a criterion. The optimality conditions are explicit and do not use any constraint qualifications. For the case of a linear cost function, we reformulate the K-semidefinite problem in a regularized form and construct its dual. We show that the pair of the primal and dual regularized problems satisfies the strong duality relation which means that the duality gap is vanishing.

Exergy and sensibility analysis of each individual effect in a kraft multiple effect evaporator

TAPPI Journal ◽  
2019 ◽  
Vol 18 (10) ◽  
pp. 607-618
Author(s):  
JÉSSICA MOREIRA ◽  
BRUNO LACERDA DE OLIVEIRA CAMPOS ◽  
ESLY FERREIRA DA COSTA JUNIOR ◽  
ANDRÉA OLIVEIRA SOUZA DA COSTA
Keyword(s):  
Optimization Problem ◽  
Real Data ◽  
Kraft Pulping ◽  
Steam Temperature ◽  
Input Flow ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Multiple Effect ◽  
Sensibility Analysis ◽  
Exergetic Analysis

The multiple effect evaporator (MEE) is an energy intensive step in the kraft pulping process. The exergetic analysis can be useful for locating irreversibilities in the process and pointing out which equipment is less efficient, and it could also be the object of optimization studies. In the present work, each evaporator of a real kraft system has been individually described using mass balance and thermodynamics principles (the first and the second laws). Real data from a kraft MEE were collected from a Brazilian plant and were used for the estimation of heat transfer coefficients in a nonlinear optimization problem, as well as for the validation of the model. An exergetic analysis was made for each effect individually, which resulted in effects 1A and 1B being the least efficient, and therefore having the greatest potential for improvement. A sensibility analysis was also performed, showing that steam temperature and liquor input flow rate are sensible parameters.

Imaging through Scattering Media with a Learning Based Prior

2020 ◽  
Vol 2020 (14) ◽  
pp. 306-1-306-6
Author(s):  
Florian Schiffers ◽  
Lionel Fiske ◽  
Pablo Ruiz ◽  
Aggelos K. Katsaggelos ◽  
Oliver Cossairt
Keyword(s):  
Optimization Problem ◽  
Autonomous Driving ◽  
Scattering Media ◽  
Photon Scattering ◽  
Point Spread ◽  
Spread Function ◽  
Radiative Transport Equation ◽  
Spatio Temporal ◽  
Transient Imaging

Imaging through scattering media finds applications in diverse fields from biomedicine to autonomous driving. However, interpreting the resulting images is difficult due to blur caused by the scattering of photons within the medium. Transient information, captured with fast temporal sensors, can be used to significantly improve the quality of images acquired in scattering conditions. Photon scattering, within a highly scattering media, is well modeled by the diffusion approximation of the Radiative Transport Equation (RTE). Its solution is easily derived which can be interpreted as a Spatio-Temporal Point Spread Function (STPSF). In this paper, we first discuss the properties of the ST-PSF and subsequently use this knowledge to simulate transient imaging through highly scattering media. We then propose a framework to invert the forward model, which assumes Poisson noise, to recover a noise-free, unblurred image by solving an optimization problem.

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