Found 1606 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

A Compressed Coding Scheme for Evolutionary Algorithms in Mixed-Integer
Programming: A Case Study on Multi-Objective Constrained Portfolio
**Optimization**

Hence, the Multi-Objective Evolutionary Algorithm (MOEA), which does not require the gradient information and is efficient at dealing with the multi-objective

**optimization****problems**, is adopted frequently for these**problem**s. Expand abstract. A lot of real-world applications could be modeled as the Mixed-Integer Non-Linear Programming (MINLP) problems, and some prominent examples include portfolio optimization, resource allocation, image classification, as well as path planning. Actually, most of the models for these applications are non-convex and always involve some conflicting objectives. Hence, the Multi-Objective Evolutionary Algorithm (MOEA), which does not require the gradient information and is efficient at dealing with the multi-objective

**optimization**problems, is adopted frequently for these**problems**. In this work, we discuss the coding scheme for MOEA in MINLP, and the major discussion focuses on the constrained portfolio**optimization**problem, which is a classic financial**problem**and could be naturally modeled as MINLP. As a result, the challenge, faced by a direct coding scheme for MOEA in MINLP, is pointed out that the searching in multiple search spaces is very complicated. Thus, a Compressed Coding Scheme (CCS), which converts an MINLP**problem**into a continuous problem, is proposed to address this challenge. The analyses and experiments on 20 portfolio benchmark instances, of which the number of available assets ranging from 31 to 2235, consistently indicate that CCS is not only efficient but also robust for dealing with the constrained multi-objective portfolio**optimization**.85 days ago

8/10 relevant

arXiv

8/10 relevant

arXiv

On optimum design of frame structures

Finally, we solve three sample

**optimization****problems**and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. Expand abstract.**Optimization**of frame structures is formulated as a~non-convex

**optimization**problem, which is currently solved to local optimality. In this contribution, we investigate four

**optimization**approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial

**optimization**. We show that polynomial

**optimization**solves the frame structure

**optimization**to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample

**optimization**

**problems**and conclude that the local

**optimization**approaches may indeed converge to local optima, without any solution quality measure, or even to infeasible points. These issues are readily overcome by using polynomial optimization, which exhibits a finite convergence, at the prize of higher computational demands.

87 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Learning adiabatic quantum algorithms for solving **optimization** **problems**

In this paper we propose a hybrid quantum-classical algorithm to solve

**optimization****problems**with an adiabatic machine assuming restrictions on the class of available**problem**Hamiltonians. Expand abstract. An adiabatic quantum algorithm is essentially given by three elements: An initial Hamiltonian with known ground state, a

**problem**Hamiltonian whose ground state corresponds to the solution of the given**problem**and an evolution schedule such that the adiabatic condition is satisfied. A correct choice of these elements is crucial for an efficient adiabatic quantum computation. In this paper we propose a hybrid quantum-classical algorithm to solve**optimization****problems**with an adiabatic machine assuming restrictions on the class of available**problem**Hamiltonians. The scheme is based on repeated calls to the quantum machine into a classical iterative structure. In particular we present a technique to learn the encoding of a given**optimization****problem**into a**problem**Hamiltonian and we prove the convergence of the algorithm. Moreover the output of the proposed algorithm can be used to learn efficient adiabatic algorithms from examples.88 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Copositive certificates of non-negativity for polynomials on semialgebraic sets

Last but not least, copositive certificates can be used to obtain not only hierarchies of tractable lower bounds, but also hierarchies of tractable upper bounds for polynomial

**optimization****problems**. Expand abstract. A certificate of non-negativity is a way to write a given function so that its non-negativity becomes evident. Certificates of non-negativity are fundamental tools in optimization, and they underlie powerful algorithmic techniques for various types of

**optimization****problems**. We propose certificates of non-negativity of polynomials based on copositive polynomials. The certificates we obtain are valid for generic semialgebraic sets and have a fixed small degree, while commonly used sums-of-squares (SOS) certificates are guaranteed to be valid only for compact semialgebraic sets and could have large degree.**Optimization**over the cone of copositive polynomials is not tractable, but this cone has been well studied. The main benefit of our copositive certificates of non-negativity is their ability to translate results known exclusively for copositive polynomials to more general semialgebraic sets. In particular, we show how to use copositive polynomials to construct structured (e.g., sparse) certificates of non-negativity, even for unstructured semialgebraic sets. Last but not least, copositive certificates can be used to obtain not only hierarchies of tractable lower bounds, but also hierarchies of tractable upper bounds for polynomial**optimization****problems**.89 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

**Optimization** Based Motion Planning for Multi-Limbed Vertical Climbing
Robots

The first part can be formulated as either a mixed-integer convex programming (MICP) or NLP

**problem**, while the second part is formulated as a series of standard convex**optimization****problems**. Expand abstract. Motion planning trajectories for a multi-limbed robot to climb up walls requires a unique combination of constraints on torque, contact force, and posture. This paper focuses on motion planning for one particular setup wherein a six-legged robot braces itself between two vertical walls and climbs vertically with end effectors that only use friction. Instead of motion planning with a single nonlinear programming (NLP) solver, we decoupled the

**problem**into two parts with distinct physical meaning: torso postures and contact forces. The first part can be formulated as either a mixed-integer convex programming (MICP) or NLP problem, while the second part is formulated as a series of standard convex**optimization****problems**. Variants of the two wall climbing**problem**e.g., obstacle avoidance, uneven surfaces, and angled walls, help verify the proposed method in simulation and experimentation.90 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Riemannian Proximal Gradient Methods

In the Euclidean setting the proximal gradient method and its accelerated variants are a class of efficient algorithms for optimization problems with decomposable objective. Expand abstract.

In the Euclidean setting the proximal gradient method and its accelerated variants are a class of efficient algorithms for

**optimization****problems**with decomposable objective. However, due to the lack of linearity on a generic manifold, studies on such methods for similar**problems**but constrained on a manifold are still limited. In this paper we develop and analyze a generalization of the proximal gradient methods with and without acceleration for**problems**on Riemannian manifolds. Global convergence of the Riemannian proximal gradient method has been established under mild assumptions. The $O(1/k)$ and $O(1/k^2)$ convergence rate analyses are also derived for the method and its accelerated variant provided more assumptions hold. To the best of our knowledge, this is the first attempt to establish the convergence rate of the Riemannian proximal gradient methods for the nonsmooth Riemannian**optimization****problem**. Empirical performance comparisons show that the proposed Riemannian proximal gradient methods are competitive with existing ones.90 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Collective dynamics of phase-repulsive oscillators solves graph coloring
**problem**

Recent years saw a fast development of quantum algorithms that solve combinatorial

**optimization****problems**, such as graph coloring, by finding the ground state of a suitable quantum system. Expand abstract. Recent years saw a fast development of quantum algorithms that solve combinatorial

**optimization**problems, such as graph coloring, by finding the ground state of a suitable quantum system. Inspired by this, we show how to couple phase-oscillators on a graph so that collective dynamics `searches' for the coloring of that graph as it relaxes towards the dynamical equilibrium. This translates a combinatorial**optimization****problem**(graph coloring) into a continuous**optimization****problem**(finding and evaluating the global minimum of dynamical non-equilibrium potential, done by the natural system's evolution). Using a sample of graphs we show that our method performs at least as good as traditional combinatorial algorithms and can serve as a viable alternative to them. Moreover, we show that with the same computational cost our method efficiently solves the harder**problem**of improper coloring of weighed graphs.90 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

On existence of optimal potentials on unbounded domains

These

**problem**s can be seen as the natural extension of shape**optimization****problems**to the framework of potentials. Expand abstract. We consider elliptic equations of Schr\"odinger type with a right-hand side fixed and with the linear part of order zero given by a potential V . The main goal is to study the

**optimization****problem**for an integral cost depending on the solution uV , when V varies in a suitable class of admissible potentials. These**problems**can be seen as the natural extension of shape**optimization****problems**to the framework of potentials. The main result is an existence theorem for optimal potentials, and the main difficulty is to work in the whole Euclidean space Rd, which implies a lack of compactness in several crucial points. In the last section we present some numerical simulations.90 days ago

7/10 relevant

arXiv

7/10 relevant

arXiv

Online Linear Programming: Dual Convergence, New Algorithms, and Regret Bounds

We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are generated i.i.d. from an unknown distribution and revealed sequentially over time. Expand abstract.

We study an online linear programming (OLP)

**problem**under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are generated i.i.d. from an unknown distribution and revealed sequentially over time. Virtually all current online algorithms were based on learning the dual optimal solutions/prices of the linear programs (LP), and their analyses were focused on the aggregate objective value and solving the packing LP where all coefficients in the constraint matrix and objective are nonnegative. However, two major open questions are: (i) Does the set of LP optimal dual prices in OLP converge to those of the "offline" LP, and (ii) Could the results be extended to general LP**problems**where the coefficients can be either positive or negative. We resolve these two questions by establishing convergence results for the dual prices under moderate regularity conditions for general LP**problems**. Then we propose a new type of OLP algorithm, Action-History-Dependent Learning Algorithm, which improves the previous algorithm performances by taking into account the past input data as well as and decisions/actions already made. We derive an $O(\log n \log \log n)$ regret bound for the proposed algorithm, against the $O(\sqrt{n})$ bound for typical dual-price learning algorithms, and show that no dual-based thresholding algorithm achieves a worst-case regret smaller than $O(\log n)$, where n is the number of decision variables. Numerical experiments demonstrate the superior performance of the proposed algorithms and the effectiveness of our action-history-dependent design. Our results also indicate that, for solving online**optimization****problems**with constraints, it's better to utilize a non-stationary policy rather than the stationary one.91 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Extending FISTA to Riemannian **Optimization** for Sparse PCA

Since the

**optimization****problem**is essentially non-convex, a safeguard strategy is introduced in the algorithm. Expand abstract. Sparse PCA, an important variant of PCA, attempts to find sparse loading vectors when conducting dimension reduction. This paper considers the Riemannian

**optimization****problem**related to the ScoTLASS model for sparse PCA which can impose orthogonality and sparsity simultaneously. We extend FISTA from the Euclidean space to the Riemannian manifold to solve this**problem**. Since the**optimization****problem**is essentially non-convex, a safeguard strategy is introduced in the algorithm. Numerical evaluations establish the computational advantages of the algorithm over the existing proximal gradient methods on manifold. Convergence of the algorithm to stationary points has also been rigorously justified.91 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv