An interior-point algorithm for linear optimization based on a new algebraically equivalent transformation

Interior-point algorithm for linear optimization based on a new trigonometric kernel function

We present an analysis of the full-Newton step infeasible interior-point algorithm for semidefinite optimization, which is an extension of the algorithm introduced by Roos [C. Roos, A full-Newton step 𝒪(n) infeasible interior-point algorithm for linear optimization, SIAM J. Optim. 16 (2006), pp. 1110–1136] for the linear optimization case. We use the proximity measure σ(V) = ‖I − V 2‖ to overcome the difficulty of obtaining an upper bound of updated proximity after one full-Newton step, where I is an identity matrix and V is a symmetric positive definite matrix. It turns out that the complexity analysis of the algorithm is simplified and the iteration bound obtained is improved slightly.

An interior-point algorithm for linear optimization based on a new barrier function

In this paper, we propose a theoretical framework of a predictor-corrector interior-point method for linear optimization based on the one-norm wide neighborhood of the central path, focusing on infeasible corrector steps. Here, we call the predictor-infeasible corrector algorithm. At each iteration, the proposed algorithm computes an infeasible corrector step in addition to the Ai-Zhang search directions and considers the Newton direction as a linear combination of these directions. We represent the complexity analysis of the algorithm and conclude that its iteration bound is $${\mathcal {O}}(n\log \varepsilon ^{-1})$$ . To our knowledge, this is the best complexity result up to now for infeasible interior-point methods based on these kinds of search directions. The complexity bound obtained here is the same as small neighborhood infeasible interior point algorithms.

Kernel functions serve the central goal of creating new search directions for the primal-dual interiorpoint algorithm to solve linear optimization problems. A significantly improved primal-dual interior-point algorithm for linear optimization is presented based on a novel kernel function. We show a primal-dual interior-point technique for linear optimization based on a class of kernel functions that are eligible. This research presents a new efficient kernel function-based primal-dual IPM algorithm for semidefinite programming problems based on the Nesterov-Todd (NT) direction. With a new and simple technique, we propose a new kernel function to obtain an optimal solution of the perturbed problem (SDP)µ. We obtain the best-known complexity results,for smalland large-update namely O(pp+1/2p √nlog tr(X0S0)/ε) and O((pn)p+1/2p log trX0S0/ε) large update To prove the effectiveness of our proposed kernel function, we compare our numerical results with some alternatives presented by Touil et al. (2017).

Based on an equivalent reformulation of the central path, we obtaina modified-Newton step for linear optimization. Using this step, wepropose an infeasible interior-point algorithm. The algorithm usesonly one full-modified-Newton step search in each iteration. Thecomplexity bound of the algorithm is the best known for infeasibleinterior-point algorithm.

Based on a new parametric kernel function, this paper presents a primal-dual large-update interior-point algorithm (IPM) for semi-definite optimization (SDO) problems. The new parametric function is neither self-regular function nor the usual logarithmic barrier function. It is strongly convex and possesses some novel analytic properties. We analyse this new parametric kernel function and show that the proposed algorithm has favorable complexity bound in terms of the analytic properties of the kernel function. Moreover, the complexity bound for our large-update IPM is shown to be O(\sqrt{n}(\log n)^2 \log\frac{n}{\epsilon}). Some numerical results are reported to illustrate the feasibility of the proposed algorithm.

In this paper, we propose a new predictor–corrector interior-point algorithm for semidefinite optimization based on a wide neighbourhood of the central path. We show that, in addition to the predictor step, each corrector step decreases the duality gap as well. We also prove that the iteration complexity of the proposed algorithm coincides with the best iteration bound for small neighbourhood algorithms that use the Nesterov–Todd direction. Finally, some numerical results are provided as well.

The inverse problem concerning electromagnetic casting of molten metals consists of looking for an electric current density distribution such that the induced electromagnetic field makes a given mass of liquid metal acquire a predefined shape. This problem is formulated here as an optimization problem where the positions of a finite set of inductors are the design variables. Two different formulations for this optimization problem for the two-dimensional case are proposed. The first one minimizes the difference between the target and the equilibrium shapes while the second approach minimizes the L2 norm of a fictitious surface pressure that makes the target shape to be in mechanical equilibrium. The optimization problems are solved using Feasible Arc Interior Point Algorithm, a line search interior-point algorithm for nonlinear optimization. Some examples are presented to show the effectiveness of the proposed approaches.

In this paper, a full Nesterov–Todd-step infeasible interior-point algorithm is presented for semidefinite optimization (SDO) problems. In contrast of some classical interior-point algorithms for SDO problems, this algorithm does not need to perform computationally expensive calculations for centering steps which are needed for classical interior-point methods. The convergence analysis of the algorithm is shown and it is also proved that the complexity bound of the algorithm coincides with the currently best iteration bound obtained by infeasible interior-point algorithms for this class of optimization problems.

In this paper, a new algorithm for convex quadratic programming (QP) is presented. Firstly, the surrogate problem for QP is developed, and the Karush-Kuhn-Tucker conditions of the surrogate problem hold if the unconstrained minimum of the objective function does not satisfy any constraints. Then, Karmarkar's algorithm for linear programming (LP) is introduced to solve the surrogate dual problem. In addition, the case of general constraints is also discussed, and some examples of optimum truss sizing problems show that the proposed algorithm is robust and efficient.

A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer structures considering internal heating. The model leverages a closed-form analytical forward solution to enable efficient inverse computations. It requires only a single internal temperature measurement as input, with unknown parameters estimated by minimizing an objective function using an interior-point optimization algorithm. The IHCM accurately identifies thermal properties such as thermal conductivity, specific heat capacity, density, and heat transfer coefficient in a high-precision linear motor. It also detects internal geometric variations, including the location and severity of delamination caused by thermal expansion. These predictions are validated against finite element (FE) simulations. Furthermore, a sensorless strategy is proposed, enabling non-invasive parameter estimation based on electrically inferred temperature data. The feasibility, sensitivity, and limitations of the IHCM are assessed across various scenarios. Results demonstrate its strong potential for real-time diagnostics, online defect detection, and thermal performance monitoring in multi-layer composite systems with internal heat generation, such as electrical machines. • Fast inverse parameter estimation in multilayer composites with internal heating. • Diagnoses thermal aging and detects global and local delamination. • Flexible analytical forward framework for multiple non-homogeneities. • High computational speed enables real-time, lightweight thermal diagnosis. • Noninvasive, sensorless estimation through electrically inferred temperature.

This paper presents a decomposed co-design optimization framework to jointly design the geometry and the controller of a Continuously Variable Transmission (CVT), accounting for its low-level dynamics. Specifically, we first devise a model of the CVT and the feedback controller, and use it to formulate the optimal co-design problem with the goal of minimizing the transmission's mass as well as the losses that occur in the system, including the lower-level actuation. Second, we divide the resulting nonlinear multi-objective optimization problem into separate hierarchical optimization subproblems and we leverage the concept of Analytical Target Cascading (ATC) to solve the separate optimization subproblems using an interior-point optimization algorithm. Finally, we showcase our framework on a representative drive cycle. Our results demonstrate that the presented co-design method can achieve a more compact CVT design without compromising the desired ratio trajectory and reducing the overall losses by up to 14%.

We propose an integrated modeling and optimization framework including detailed computational fluid dynamics based models and polymer electrolyte membrane fuel cell (PEMFC) systems. As an illustration, a multidimensional, multiphysics PEMFC model is constructed that accounts for major transport processes in the gas channels and the membrane electrode assembly. The resulting system of highly nonlinear partial differential‐algebraic equations is fully discretized using a finite volume method, and the resulting large‐scale nonlinear program is linked to a state‐of‐the‐art interior point optimization algorithm. The framework is used for solving challenging parameter estimation problems resulting from incorporation of multiple experimental data points. Also, parametric studies are performed on detailed water transport mechanisms and distribution characteristics, and on overall system performance. Our proposed framework provides a robust and fast solution methodology, and is planned for modeling extensions and addressing other critical issues in PEMFC technology that require large‐scale simulations. © 2008 American Institute of Chemical Engineers AIChE J, 2008

Under the background of the national dual carbon strategy, it is very necessary for power enterprises to give full play to their subjective initiative and carry out the research on the optimization strategy of carbon emission reduction based on the allocation of existing power generation resources. Based on the full study of the relationship between power grid power flow and carbon emission, this paper puts forward the indicators such as carbon emission per kWh and electricity carbon neutralization index, constructs the regional power grid carbon emission optimization model as a link, and uses the primal dual interior point method to optimize the unit output. Taking a typical day of a regional power grid as an example, the carbon emission reduction calculation is carried out according to the two stages of unified dispatching unit optimization and self owned power plant optimization. The relevant results show that the carbon emission indicators proposed in this paper can well characterize the carbon emission level of the regional power grid, the carbon emission optimization model is accurate and reliable, and the optimization strategy results can be used as an important reference for the carbon emission reduction of power grid regulators [1].