Journal of Optimization Theory and Applications最新文献

In this paper, an improved retractable body model (IRBM) is established, which has an advantage in simulating the flexion-and-extension motion of skier’s legs during carved turning and straight gliding. The trajectory optimization problem for the nonlinear alpine skiing system is transformed into a multi-phase optimal control (MPOC) problem. Subsequently, a constrained multi-phase trajectory optimization model is developed based on the optimal control theory, where the optimization target is to minimize the total skiing time. The optimization model is discretized by using the Radau pseudospectral method (RPM), which transcribes the MPOC problem into a nonlinear programming (NLP) problem that is then solved by SNOPT solver. Through numerical simulations, the optimization results under different constraints are obtained using MATLAB. The variation characteristics of the variables and trajectories are analyzed, and four influencing factors related to the skiing time are investigated by comparative experiments. It turns out that the small turning radius can reduce the total skiing time, the flexion-and-extension motion of legs is beneficial to skier’s performance, and the large inclination angle can shorten skier’s turning time, while the control force has a slight effect on the skiing time. The effectiveness and feasibility of the proposed models and trajectory optimization strategies are validated by simulation and experiment results.

This paper explores the nonconvex second-order cone as a nonconvex conic extension of the known convex second-order cone in optimization, as well as a higher-dimensional conic extension of the known causality cone in relativity. The nonconvex second-order cone can be used to reformulate nonconvex quadratic programming and nonconvex quadratically constrained quadratic program in conic format. The cone can also arise in real-world applications, such as facility location problems in optimization when some existing facilities are more likely to be closer to new facilities than other existing facilities. We define notions of the algebraic structure of the nonconvex second-order cone and show that its ambient space is commutative and power-associative, wherein elements always have real eigenvalues; this is remarkable because it is not the case for arbitrary Jordan algebras. We will also find that the ambient space of this nonconvex cone is rank-independent of its dimension; this is also notable because it is not the case for algebras of arbitrary convex cones. What is more noteworthy is that we prove that the nonconvex second-order cone equals the cone of squares of its ambient space; this is not the case for all non-Euclidean Jordan algebras. Finally, numerous algebraic properties that already exist in the framework of the convex second-order cone are generalized to the framework of the nonconvex second-order cone.

This paper gives the controllability and Ulam–Hyers–Rassias (U–H–R) stability results for non-instantaneous impulsive stochastic multiple delays system with nonpermutable variable coefficients. The solution for nonlinear non-instantaneous impulsive stochastic systems is presented without the assumption of commutative property on delayed matrix coefficients. The kernel function of the solution operator is defined by sum of noncommutative products of delayed matrix constant coefficients. Sufficient conditions for controllability of linear and nonlinear non-instantaneous impulsive stochastic multiple delays system are established by using the Mönch fixed-point theorem under the proof that the corresponding linear system is controllable. Thereafter, U–H–R stability result is proved. Finally, the theoretical results are verified by a numerical example.

This paper aims to present alternative characterizations for different types of set-valued robustness concepts. Equivalent scalar representations for various set order relations are derived when the sets are the union of sets. Utilizing these findings in conjunction with image space analysis, specific isolated sets are defined for different notions of robust solutions. These isolated sets serve as the basis for deriving both necessary and sufficient robust optimality conditions. The validity of the results is demonstrated through several illustrative examples. Additionally, the paper concludes with an application of our present approach to two-player zero-sum matrix games.

The greater the persistence in a financial time series, the more predictable it becomes, allowing for the development of more effective investment strategies. Desirable attributes for financial portfolios include persistence, smoothness, long memory, and higher auto-correlation. We argue that these properties can be achieved by adjusting the composition weights of the portfolio. Considering the fractal nature of typical financial time series, the fractal dimension emerges as a natural metric to gauge the smoothness of the portfolio trajectory. Specifically, the Hurst exponent is designed for measuring the persistence of time series. In this paper, we introduce an optimization method inspired by the Hurst exponent and signal processing to mitigate the irregularities in the portfolio trajectory. We illustrate the effectiveness of this approach using real data from an S &P100 dataset.

We address the problem of minimizing a smooth function under smooth equality constraints. Under regularity assumptions on these constraints, we propose a notion of approximate first- and second-order critical point which relies on the geometric formalism of Riemannian optimization. Using a smooth exact penalty function known as Fletcher’s augmented Lagrangian, we propose an algorithm to minimize the penalized cost function which reaches (varepsilon )-approximate second-order critical points of the original optimization problem in at most ({mathcal {O}}(varepsilon ^{-3})) iterations. This improves on current best theoretical bounds. Along the way, we show new properties of Fletcher’s augmented Lagrangian, which may be of independent interest.

The usual theory of asset pricing in finance assumes that the financial strategies, i.e. the quantity of risky assets to invest, are real-valued so that they are not integer-valued in general, see the Black and Scholes model for instance. This is clearly contrary to what it is possible to do in the real world. Surprisingly, it seems that there are not many contributions in that direction in the literature, except for a finite number of states. In this paper, for arbitrary (Omega ), we show that, in discrete-time, it is possible to evaluate the minimal super-hedging price when we restrict ourselves to integer-valued strategies. To do so, we only consider terminal claims that are continuous piecewise affine functions of the underlying asset. We formulate a dynamic programming principle that can be directly implemented on historical data and which also provides the optimal integer-valued strategy. The problem with general payoffs remains open but should be solved with the same approach.

In this paper, rigid body static optimization is investigated on the Riemannian manifold of rigid body motion groups. This manifold, which is also a matrix manifold, provides a framework to formulate translational and rotational motions of the body, while considering any coupling between those motions, and uses members of the special orthogonal group (textsf{SO}(3)) to represent the rotation. Hence, it is called the special Euclidean group (textsf{SE}(3)). Formalism of rigid body motion on (textsf{SE}(3)) does not fall victim to singularity or non-uniqueness issues associated with attitude parameterization sets. Benefiting from Riemannian matrix manifolds and their metrics, a generic framework for unconstrained static optimization and a customizable framework for constrained static optimization are proposed that build a foundation for dynamic optimization of rigid body motions on (textsf{SE}(3)) and its tangent bundle. The study of Riemannian manifolds from the perspective of rigid body motion introduced here provides an accurate tool for optimization of rigid body motions, avoiding any biases that could otherwise occur in rotational motion representation if attitude parameterization sets were used.

In this paper, we investigate the asymptotic behavior of inertial dynamics with dry friction within the context of a Hilbert framework for convex differentiable optimization. Our study focuses on a doubly nonlinear first-order evolution inclusion that encompasses two potentials. In our analysis, we specifically focus on two main components: the differentiable function f that needs to be minimized, which influences the system’s state through its gradient, and the nonsmooth dry friction potential denoted as (varphi = rVert cdot Vert ). It’s important to note that the dry friction term acts on a linear combination of the velocity vector and the gradient of f. Consequently, any stationary point in our system corresponds to a critical point of f, unlike the case where only the velocity vector is involved in the dry friction term, resulting in an approximate critical point of f. To emphasize the crucial role of (nabla f(x)), we also explore the dual formulation of this dynamic, which possesses a Riemannian gradient structure. To address these dynamics, we employ the recently developed generic acceleration approach by Attouch, Bot, and Nguyen. This approach involves the time scaling of a continuous first-order differential equation, followed by the application of the method of averaging. By applying this methodology, we derive fast convergence results for second-order time-evolution systems with dry friction, asymptotically vanishing viscous damping, and implicit Hessian-driven damping.

This paper investigates an optimal reinsurance problem for an insurance company with self-exciting claims, where the insurer’s historical claims affect the claim intensity itself. We focus on a claim-dependent proportional reinsurance contact, where the term “claim-dependent” signifies that the insurer’s risk retention ratio is allowed to depend on claim size. The insurer aims to maximize the expected utility of terminal wealth. By utilizing the dynamic programming principle and verification theorem, we obtain the optimal reinsurance strategy and corresponding value function in closed-form from the Hamilton–Jacobi–Bellman equation under an exponential utility function. We show that the claim-dependent proportional reinsurance is optimal among all types of reinsurance under the exponential utility maximization criterion. In addition, we present several analytical properties and numerical examples of the derived optimal strategy and provide economic insights through analytical and numerical analyses. In particular, we show the optimal claim-dependent proportional reinsurance can be considered as a continuous approximation of the step-wise risk sharing rule between the insurer and the reinsurer.