Concave Term Research Articles

Two-Phase Robust Target Localization in Ocean Sensor Networks Using Received Signal Strength Measurements.

Target localization plays a vital role in ocean sensor networks (OSNs), in which accurate position information is not only a critical need of ocean observation but a necessary condition for the implementation of ocean engineering. Compared with other range-based localization technologies in OSNs, the received signal strength (RSS)-based localization technique has attracted widespread attention due to its low cost and synchronization-free nature. However, maintaining relatively good accuracy in an environment as dynamic and complex as the ocean remains challenging. One of the most damaging factors that degrade the localization accuracy is the uncertainty in transmission power. Besides the equipment loss, the uncertain factors in the fickle ocean environment may result in a significant deviation between the standard rated transmission power and the usable transmission power. The difference between the rated and actual transmission power would lead to an extra error when it comes to the localization in OSNs. In this case, a method that can locate the target without needing prior knowledge of the transmission power is proposed. The method relies on a two-phase procedure in which the location information and the transmission power are jointly estimated. First, the original nonconvex localization problem is transformed into an alternating non-negativity-constrained least square framework with the unknown transmission power (UT-ANLS). Under this framework, a two-stage optimization method based on interior point method (IPM) and majorization-minimization tactic (MMT) is proposed to search for the optimal solution. In the first stage, the barrier function method is used to limit the optimization scope to find an approximate solution to the problem. However, it is infeasible to approach the constraint boundary due to its intrinsic error. Then, in the second stage, the original objective is converted into a surrogate function consisting of a convex quadratic and concave term. The solution obtained by IPM is considered the initial guess of MMT to jointly estimate both the location and transmission power in the iteration. In addition, in order to evaluate the performance of IPM-MM, the Cramer Rao lower bound (CRLB) is derived. Numerical simulation results demonstrate that IPM-MM achieves better performance than the others in different scenarios.

New superstructure-based model for the globally optimal synthesis of refinery hydrogen networks

Abstract This work presents a new superstructure for refinery hydrogen networks synthesis. The superstructure eliminates the need to have the pressures of compressors as variables, while both dedicated and shared compressors can be included. As a result of considering the pressures as the parameters known a-priori, the constraint of compression power is expressed by using linear equation. Hydrogen networks synthesis is then formulated as a new mixed integer nonlinear model whose nonlinearities are only attributed to the bilinear and concave terms. The proposed model is a simple optimization problem that could be solved to global optimality. Four literature examples and an industrial case are tested for illustration purpose. The obtained solution results exhibit 3.1–4.5 % reduction in the total annualized cost compared with those of literature ones.

Matrix Factorization-Based Target Localization via Range Measurements With Uncertainty in Transmit Power

In this letter, received signal strength (RSS)- based target localization with uncertainty in transmit power (UTP) is studied. First, the localization-based alternating nonnegative constrained least squares (ANCLS) framework is conducted. A two-phase optimization method, i.e., a matrix factorization-based min-max strategy (MFMM), is then presented to figure out the solution. The first phase of optimization is based on a matrix factorization approach, i.e., active set method (ASM). However, ASM may drop to a local minimum. Therefore, a min-max strategy based on a Taylor linearization approximation is involved in the second phase, where the objective is split into a convex quadratic and a concave term. The target position and UTP are refined simultaneously in the iteration via solving a sequence of convex problems, in which the solution obtained by ASM is to be the initiation. Additionally, to evaluate the effectiveness of MFMM, both the computational complexity and the Cramer-Rao lower bound (CRLB) are analyzed. Simulations are carried out to illustrate the outperformance, compared with other state-of-the-art methods in different scenarios.

Singular (p, q)-equations with superlinear reaction and concave boundary condition

We consider a parametric nonlinear elliptic problem driven by the sum of a p-Laplacian and of a q-Laplacian (a -equation) with a singular and -superlinear reaction and a Robin boundary condition with -sublinear boundary term . So, the problem has the combined effects of singular, concave and convex terms. We look for positive solutions and prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter varies.

Anisotropic equations with indefinite potential and competing nonlinearities

We consider a nonlinear Dirichlet problem driven by a variable exponent p-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and a convex (superlinear) perturbation (the anisotropic concave–convex problem). We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter λ varies. Also, we prove the existence of minimal positive solutions.

A model-based optimization study on greywater reuse as an alternative urban water resource

Integrated urban water management (IUWM) aims to promote water supply not only from conventional sources but also from wastewater reuse in part to address issues such as water scarcity. In line with the situation, this work concerns greywater reuse in synthesizing and retrofitting water network at household and community levels. We consider various water-using activities and suitable wastewater treatment technologies through a nonlinear optimization model based on a superstructure which incorporates multiple alternatives for greywater reuse, regeneration (treatment), and recycle. The model objective aims to minimize freshwater consumption and/or wastewater generation in addition to the fixed capital cost of installing the pipes and the variable operating cost of water pumping. The optimization procedure is carried out subject to complying with constraints to reduce the contamination level to acceptable reuse limits or otherwise for disposal or discharge to the environment while meeting various real-world design and operating specifications that include requirements for minimum water service and hygienic reasons. A real-world case study is illustrated on a residential household with four occupants by combining engineering experience and physical insights to obtain a realistic model representation of the problem. To circumvent the solution challenge presented by the nonconvex formulation, we apply a convexification strategy to handle the concave terms in the objective function. The proposed approach has demonstrated that significant reductions in freshwater use are possible.

Majorization–Minimization-Based Target Localization Problem From Range Measurements

In this letter, received signal strength (RSS) based target localization is studied. First we start with the case of known emitted power of target. The least squares (LS) approach is adopted, and the object function is shown to be decomposed as a convex quadratic plus a concave term. Consequently, a Majorization-Minimization (MM) based approach from range measurements termed R-MM is proposed, which iteratively finds the local optimum through simple operations. To further improve the performance, unconstrained squared-range (USR)-based LS estimation is used as an initial point for R-MM, named R-MM-USR. Then R-MM-USR is extended to solve the target localization under unknown emitted power through alternating minimization. For both cases Cramer Rao bound (CRB) is derived. In addition, the computation complexity of R-MM-USR is lowest among the high accuracy approaches. Besides, numerical simulations are conducted to demonstrate the near optimal performance, compared with CRB and other state-of-art methods.

Positive solutions for ( p , 2 ) -equations with superlinear reaction and a concave boundary term

Positive solutions for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mi>,</mml:mi> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:math>-equations with superlinear reaction and a concave boundary term

Multiple solutions with sign information for a [formula omitted]-equation with combined nonlinearities

We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.

Nonlinear singular problems with indefinite potential term

We consider a nonlinear Dirichlet problem driven by a nonhomogeneous differential operator plus an indefinite potential. In the reaction we have the competing effects of a singular term and of concave and convex nonlinearities. In this paper the concave term will be parametric. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the positive parameter lambda varies.

Multiple Solutions for {varvec{(p,2)}}-Equations with Resonance and Concave Terms

We consider parametric Dirichlet problems driven by the sum of a p-Laplacian (p>2) and a Laplacian ((p, 2)-equation) and with a reaction term which exhibits competing nonlinearities. We prove two multiplicity theorems. In the first the competing terms are not decoupled, the dependence on the parameter is not necessarily linear and the reaction term has a general polynomial growth, possibly supercritical. We produce three nontrivial solutions for small values of the parameter. We provide sign information for all solutions (two of constant sign and the third nodal). Then we decouple the competing nonlinearities and allow for resonance to occur at pm ,infty . We produce six nontrivial smooth solutions for small values of the parameter. We provide sign information for five of these solutions.

On Kirchhoff Problems Involving Critical Exponent and Critical Growth

In this paper, we establish the existence of multiple solutions to a class of Kirchhoff type equations involving critical exponent, concave term and critical growth. Our main tools are the Nehari manifold and mountain pass theorem.

Noncoercive resonant (p,2)-equations with concave terms

AbstractWe consider a nonlinear Dirichlet problem driven by the sum of ap-Laplace and a Laplacian (a(p,2){(p,2)}-equation). The reaction exhibits the competing effects of a parametric concave term plus a Caratheodory perturbation which is resonant with respect to the principle eigenvalue of the Dirichletp-Laplacian. Using variational methods together with truncation and comparison techniques and Morse theory (critical groups), we show that for all small values of the parameter, the problem has as least six nontrivial smooth solutions all with sign information (two positive, two negative and two nodal (sign changing)).

Asymmetric Robin Problems with Indefinite Potential and Concave Terms

Abstract We consider a parametric semilinear Robin problem driven by the Laplacian plus an indefinite and unbounded potential. In the reaction, we have the competing effects of a concave term appearing with a negative sign and of an asymmetric asymptotically linear term which is resonant in the negative direction. Using variational methods together with truncation and perturbation techniques and Morse theory (critical groups), we prove two multiplicity theorems producing four and five, respectively, nontrivial smooth solutions when the parameter λ &gt; 0 {\lambda&gt;0} is small.

Nodal Solutions for Nonlinear Non-Homogeneous Robin Problems with an Indefinite Potential

AbstractWe consider a nonlinear Robin problem driven by a non-homogeneous differential operator plus an indefinite potential term. The reaction function is Carathéodory with arbitrary growth near±∞. We assume that it is odd and exhibits a concave term near zero. Using a variant of the symmetric mountain pass theorem, we establish the existence of a sequence of distinct nodal solutions which converge to zero.

Systematic Currency Volatility Risk Premia

I show that volatility risk of the dollar factor --- an equally weighted basket of developed U.S. dollar exchange rates --- carries a significant risk premium and that it is priced in the cross-section of currency volatility excess returns. The dollar factor volatility risk premium is negative on average with an upward sloping and concave term structure. Consistent with this pattern, I find that dollar factor volatility risk is most significantly priced in the cross-section of volatility excess returns at shorter maturities. A trading strategy that sells (buys) volatility insurance on currencies with high (low) exposure to dollar factor volatility risk delivers high mean excess returns and Sharpe ratios. At shorter maturities, the profitability of this strategy cannot be explained by exposure to traditional currency factors, equity factors, or currency volatility carry factors.

On a $(p,q)$-Laplacian problem with parametric concave term and asymmetric perturbation

A Dirichlet problem driven by the (p,q) -Laplace operator and an asymmetric concave reaction with positive parameter is investigated. Four nontrivial smooth solutions (two positive, one negative, and the remaining nodal) are obtained once the parameter turns out to be suffciently small. Under a oddness condition near the origin for the perturbation, a whole sequence of sign-changing solutions, which converges to zero, is produced.

(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms

We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.

Positive solutions for resonant (&lt;i&gt;p&lt;/i&gt;, &lt;i&gt;q&lt;/i&gt;)-equations with concave terms

We consider a parametric (p, q)-equation with competing nonlinearities in the reaction. There is a parametric concave term and a resonant Caratheordory perturbation. The resonance is with respect to the principal eigenvalue and occurs from the right. So the energy functional of the problem is indefinite. Using variational tools and truncation and comparison techniques we show that for all small values of the parameter the problem has at least two positive smooth solutions.

Optimal Power Flow of Radial Networks and Its Variations: A Sequential Convex Optimization Approach

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the $\varepsilon $ -constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.